From f9482747b8f438d05b55febfd2739c72fe2f208b Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Wed, 1 Nov 2023 19:27:06 -0400 Subject: [PATCH 01/19] Initial implementation of simplified SBM. Working on global opt problems, but need termination criteria for local opt. --- _test/test_eopt_solvers.py | 11 +- cert_tools/eopt_solvers.py | 203 +++++++++++++++++++++++++++++++++++++ 2 files changed, 211 insertions(+), 3 deletions(-) diff --git a/_test/test_eopt_solvers.py b/_test/test_eopt_solvers.py index c8c621e..28b1436 100644 --- a/_test/test_eopt_solvers.py +++ b/_test/test_eopt_solvers.py @@ -251,7 +251,7 @@ def test_mw_localize(): test_eopt(prob_file="test_prob_3.pkl", global_min=False, opts=opts) test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts=opts) test_eopt(prob_file="test_prob_5.pkl", global_min=False, opts=opts) - test_eopt(prob_file="test_prob_7.pkl", global_min=True, opts=dict()) + test_eopt(prob_file="test_prob_7.pkl", global_min=True, opts=opts) def test_polynomials(): @@ -275,9 +275,9 @@ def test_polynomials(): def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): - print(f"======={prob_file} -- cutting plane ==========") - from cert_tools.eopt_solvers import opts_cut_dflt, opts_sub_dflt + from cert_tools.eopt_solvers import opts_cut_dflt, opts_sub_dflt, opts_sbm_dflt + print(f"======={prob_file} -- cutting plane ==========") opts_cut_dflt.update(opts) run_eopt( prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" @@ -287,6 +287,11 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): run_eopt( prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" ) + print(f"======={prob_file} -- spectral bundle ==========") + opts_sbm_dflt.update(opts) + run_eopt( + prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sbm" + ) if __name__ == "__main__": diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 89f134e..6b0bdba 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -47,6 +47,18 @@ # starting value for alpha backtrack_start = 10.0 +# Options for Spectral Bundle Method +opts_sbm_dflt = dict( + tol_eig=1e-6, # Eigenvalue tolerance + max_iter=1000, # Maximum iterations + tol_null=1e-5, # null space tolerance for first order KKT constraints + use_null=True, # if true, reparameterize problem using null space + rho_trust=1e-1, # penalty parameter to ensure closeness to trust region. + r_c=1, # Number of current eigenvectors to keep + r_p=0, # Number of previous eigenvectors to keep + debug=True, # Debugging flag +) + class CutPlaneModel: """This class stores all of the information of the cutting plane model. @@ -347,6 +359,8 @@ def solve_eopt( solver = solve_eopt_cuts elif method == "sub": solver = solve_eopt_sub + elif method == "sbm": + solver = solve_eopt_sbm else: raise ValueError(f"Unknown method {method} in solve_eopt") @@ -603,6 +617,195 @@ def solve_eopt_cuts( ) +class SpectralBundleModel: + """SpectralBundleModel class stores all of the information associated with the spectral bundle method for eigenvalue optimization. It also stores methods for updating these variables.""" + + def __init__(m, Q, A_vec, V_init, opts=opts_sbm_dflt): + # Check that the null space has been removed + if not opts["use_null"]: + raise ValueError( + "Spectral Bundle method requires that the eigenvalue problem is unconstrained. Please preprocess to remove constraints." + ) + # Store shape + m.n_vars = A_vec.shape[1] + m.n_x = Q.shape[0] + # Store constraints and cost + m.Q = Q + m.A_vec = A_vec + # Define aggregate matrix variables + # TODO: This needs to be changed for the case of r_bar > 1 + m.A_X = m.eval_A_X(V_init) + m.Q_X = V_init.T @ Q @ V_init + # Define the eigenvector matrix + m.V = V_init + # Store Options + m.opts = opts + # Debug variables + if opts["debug"]: + # Store actual X + m.X = V_init @ V_init.T + + def eval_A_X(m, V): + A_X_list = [] + for i in range(m.n_vars): + A = m.A_vec[:, i].reshape((m.n_x, m.n_x), order="F") + if V.shape[0] == V.shape[1]: + A_X_list += [np.trace(A @ V)] + else: + A_X_list += [V.T @ A @ V] + return np.vstack(A_X_list) + + def update_vars(m, u, eta, x_prev, grad_info): + """update aggregate matrix variables""" + # TODO: Currently only implemented for scalar 'u' variable + if m.opts["debug"]: + m.X = eta * m.X + u * grad_info["min_vec"] @ grad_info["min_vec"].T + # Update agreggate variables + m.A_X = eta * m.A_X + u * grad_info["subgrad"] + m.Q_X = eta * m.Q_X + u * grad_info["min_vec"].T @ m.Q @ grad_info["min_vec"] + # Update null space multipliers (simplified because agg X is optimal X) + x = x_prev + m.A_X / m.opts["rho_trust"] + return x + + def solve_sbm_qp(m, x_curr, grad_info): + """Solve Spectral Bundle method subproblem for the case where the SDP variable + is scalar.""" + + # VARIABLES + u = cp.Variable() + eta = cp.Variable() + # CONSTRAINTS + constraints = [u + eta <= 1.0, u >= 0.0, eta >= 0.0] + # Objective + obj = ( + eta * (m.Q_X + m.A_X.T @ x_curr) + + u * grad_info["min_eig"] + + cp.sum_squares(eta * m.A_X + u * grad_info["subgrad"]) + / 2 + / m.opts["rho_trust"] + ) + # Solve Quadratic Program: + prob = cp.Problem(cp.Minimize(obj), constraints) + try: + prob.solve(solver="MOSEK", verbose=False) + except mosek.Error: + print("Did not find MOSEK, using different solver.") + prob.solve(solver="CVXOPT", verbose=False) + # Get solution + return u.value, eta.value + + +def solve_eopt_sbm( + Q, + A_vec, + xinit, + A_eq=None, + b_eq=None, + verbose=True, + opts=opts_sbm_dflt, + kwargs_eig={}, +): + """Solve Eigenvalue Optimization using the spectral bundle method. + + Args: + Q (_type_): _description_ + A_vec (_type_): _description_ + xinit (_type_): _description_ + A_eq (_type_, optional): _description_. Defaults to None. + b_eq (_type_, optional): _description_. Defaults to None. + verbose (bool, optional): _description_. Defaults to True. + opts (_type_, optional): _description_. Defaults to opts_cut_dflt. + kwargs_eig (dict, optional): _description_. Defaults to {}. + """ + # Intialize status vars for optimization + status = "RUNNING" + header_printed = False + n_iter = 0 + x_curr = xinit + t_max = np.inf + t_min = -np.inf + iter_info = [] + grad_info = None + m = None + while status == "RUNNING": + # GET CERTIFICATE AND GRADIENT INFO + # Construct Current Certificate matrix + H = get_cert_mat(Q, A_vec, x_curr) + # current gradient and minimum eig + grad_info = get_grad_info(H=H, A_vec=A_vec, **kwargs_eig) + # SOLVE SPECTRAL BUNDLE PROGRAM + if n_iter > 0: + if opts["r_c"] == 1 and opts["r_p"] == 0: + u, eta = m.solve_sbm_qp(x_curr=x_curr, grad_info=grad_info) + else: + raise NotImplementedError + # Update variables + x_prev = x_curr.copy() + x_curr = m.update_vars(u=u, eta=eta, x_prev=x_prev, grad_info=grad_info) + delta_x = x_curr - x_prev + else: + # Initialize SBM model + m = SpectralBundleModel(Q, A_vec, grad_info["min_vec"], opts=opts) + delta_x = np.zeros(x_curr.shape) + + # STATUS UPDATE + # update model upper bound + # TODO there is probably a way of computing this from the model. + # if t_ub <= t_max: + # t_max = t_ub + # update model lower bound + if grad_info["min_eig"] > t_min: + t_min = grad_info["min_eig"] + # termination criteria + if t_min >= -opts["tol_eig"]: # positive lower bound + status = "POS_LB" + elif m.n_vars == 0: # no variables (i.e. no redundant constraints) + status = "NO_VAR" + elif t_max < -2 * opts["tol_eig"]: # negative upper bound + status = "NEG_UB" + elif n_iter >= opts["max_iter"]: # max iterations + status = "MAX_ITER" + # plot_along_grad(Q, A_vec, x_new, grad_info["subgrad"], 1) + # Statistics + gap = t_max - t_min + delta_norm = la.norm(delta_x) + # Store data + info = dict( + n_iter=n_iter, + delta_norm=delta_norm, + x=x_curr, + min_eig_curr=grad_info["min_eig"], + t_max=t_max, + t_min=t_min, + gap=gap, + mult=grad_info["t"], + ) + iter_info += [info] + if verbose: + if n_iter % 10 == 0: + header_printed = False + if header_printed is False: + print(" N | delta_nrm | eig val | t_max |", end="") + print(" t_min | gap | mult. |") + header_printed = True + print( + f" {n_iter:3d} | {delta_norm:5.4e} | {grad_info['min_eig']:5.4e} | {t_max:5.4e} |", + end="", + ) + print(f"{t_min:5.4e} | {gap:5.4e} | {grad_info['t']:4d}") + # Update Iterations + n_iter += 1 + return x_curr, dict( + min_eig=grad_info["min_eig"], + H=H, + status=status, + gap=gap, + t_min=t_min, + t_max=t_max, + iter_info=pd.DataFrame(iter_info), + ) + + def get_cert_mat(C, A_vec, mults, sparsify=True, exploit_centered=False): """Generate certificate matrix from cost, constraints and multipliers C is the cost matrix amd A_vec is expected to be a vectorized version From 60832c2765bccc7eee8b63c2ed9be49c4c541d0d Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Thu, 2 Nov 2023 13:59:35 -0400 Subject: [PATCH 02/19] Added status check for negative model eigenvalue. Fixed case when no redundant constraints are available. --- cert_tools/eopt_solvers.py | 115 ++++++++++++++++++++++--------------- 1 file changed, 68 insertions(+), 47 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 6b0bdba..074d7ea 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -50,10 +50,12 @@ # Options for Spectral Bundle Method opts_sbm_dflt = dict( tol_eig=1e-6, # Eigenvalue tolerance + tol_gap=1e-7, # gap between model and actual eigenvalue for convergence max_iter=1000, # Maximum iterations tol_null=1e-5, # null space tolerance for first order KKT constraints use_null=True, # if true, reparameterize problem using null space - rho_trust=1e-1, # penalty parameter to ensure closeness to trust region. + rho_pen=1e-2, # penalty parameter to ensure closeness to trust region. + ser_step_mult=0.0, # multiplier for "serious step" r_c=1, # Number of current eigenvectors to keep r_p=0, # Number of previous eigenvectors to keep debug=True, # Debugging flag @@ -632,18 +634,19 @@ def __init__(m, Q, A_vec, V_init, opts=opts_sbm_dflt): # Store constraints and cost m.Q = Q m.A_vec = A_vec - # Define aggregate matrix variables - # TODO: This needs to be changed for the case of r_bar > 1 - m.A_X = m.eval_A_X(V_init) - m.Q_X = V_init.T @ Q @ V_init # Define the eigenvector matrix m.V = V_init # Store Options m.opts = opts - # Debug variables - if opts["debug"]: - # Store actual X - m.X = V_init @ V_init.T + if m.n_vars > 0: + # Define aggregate matrix variables + # TODO: This needs to be changed for the case of r_bar > 1 + m.A_X = m.eval_A_X(V_init) + m.Q_X = V_init.T @ Q @ V_init + # Debug variables + if opts["debug"]: + # Store actual X + m.X = V_init @ V_init.T def eval_A_X(m, V): A_X_list = [] @@ -655,16 +658,20 @@ def eval_A_X(m, V): A_X_list += [V.T @ A @ V] return np.vstack(A_X_list) - def update_vars(m, u, eta, x_prev, grad_info): + def update_vars(m, opt_info, x_prev, grad_info): """update aggregate matrix variables""" # TODO: Currently only implemented for scalar 'u' variable + # Get optimization information + u = opt_info["u"] + eta = opt_info["eta"] + # Store big X if debugging if m.opts["debug"]: m.X = eta * m.X + u * grad_info["min_vec"] @ grad_info["min_vec"].T # Update agreggate variables m.A_X = eta * m.A_X + u * grad_info["subgrad"] m.Q_X = eta * m.Q_X + u * grad_info["min_vec"].T @ m.Q @ grad_info["min_vec"] # Update null space multipliers (simplified because agg X is optimal X) - x = x_prev + m.A_X / m.opts["rho_trust"] + x = x_prev + m.A_X / m.opts["rho_pen"] return x def solve_sbm_qp(m, x_curr, grad_info): @@ -682,7 +689,7 @@ def solve_sbm_qp(m, x_curr, grad_info): + u * grad_info["min_eig"] + cp.sum_squares(eta * m.A_X + u * grad_info["subgrad"]) / 2 - / m.opts["rho_trust"] + / m.opts["rho_pen"] ) # Solve Quadratic Program: prob = cp.Problem(cp.Minimize(obj), constraints) @@ -692,7 +699,12 @@ def solve_sbm_qp(m, x_curr, grad_info): print("Did not find MOSEK, using different solver.") prob.solve(solver="CVXOPT", verbose=False) # Get solution - return u.value, eta.value + opt_info = dict( + u=u.value, + eta=eta.value, + obj_val=obj.value, + ) + return opt_info def solve_eopt_sbm( @@ -722,61 +734,71 @@ def solve_eopt_sbm( header_printed = False n_iter = 0 x_curr = xinit - t_max = np.inf - t_min = -np.inf iter_info = [] grad_info = None m = None while status == "RUNNING": - # GET CERTIFICATE AND GRADIENT INFO - # Construct Current Certificate matrix - H = get_cert_mat(Q, A_vec, x_curr) - # current gradient and minimum eig - grad_info = get_grad_info(H=H, A_vec=A_vec, **kwargs_eig) # SOLVE SPECTRAL BUNDLE PROGRAM if n_iter > 0: if opts["r_c"] == 1 and opts["r_p"] == 0: - u, eta = m.solve_sbm_qp(x_curr=x_curr, grad_info=grad_info) + opt_info = m.solve_sbm_qp(x_curr=x_curr, grad_info=grad_info) else: raise NotImplementedError # Update variables x_prev = x_curr.copy() - x_curr = m.update_vars(u=u, eta=eta, x_prev=x_prev, grad_info=grad_info) + x_curr = m.update_vars( + opt_info=opt_info, x_prev=x_prev, grad_info=grad_info + ) + # Compute change in multipliers delta_x = x_curr - x_prev + delta_norm = la.norm(delta_x) + # update model upper bound + eig_model = ( + opt_info["obj_val"][0, 0] + delta_norm**2 * opts["rho_pen"] / 2 + ) else: - # Initialize SBM model + # Init step + delta_norm = 0.0 + eig_model = np.inf + # GET CERTIFICATE AND GRADIENT INFO + # Construct Current Certificate matrix + H = get_cert_mat(Q, A_vec, x_curr) + # Update gradient and eigenvalue + if n_iter > 0: + min_eig_prev = grad_info["min_eig"] + else: + min_eig_prev = -np.inf + grad_info = get_grad_info(H=H, A_vec=A_vec, **kwargs_eig) + # Initialize model + if m is None: m = SpectralBundleModel(Q, A_vec, grad_info["min_vec"], opts=opts) - delta_x = np.zeros(x_curr.shape) - - # STATUS UPDATE - # update model upper bound - # TODO there is probably a way of computing this from the model. - # if t_ub <= t_max: - # t_max = t_ub - # update model lower bound - if grad_info["min_eig"] > t_min: - t_min = grad_info["min_eig"] + # STATUS AND VAR UPDATE + # Compute the gap + gap = eig_model - grad_info["min_eig"] + # Serious or Null Step + if grad_info["min_eig"] < min_eig_prev + opts["ser_step_mult"] * gap: + x_curr = x_prev + delta_norm = 0.0 # termination criteria - if t_min >= -opts["tol_eig"]: # positive lower bound + if grad_info["min_eig"] >= -opts["tol_eig"]: # positive lower bound status = "POS_LB" + elif eig_model < -5 * opts["tol_eig"]: # ****** EXPERIMENTAL ******* + status = "NEG_UB" + elif gap < opts["tol_gap"]: # converged eigenvalue and not positive + status = "NEG_UB" elif m.n_vars == 0: # no variables (i.e. no redundant constraints) status = "NO_VAR" - elif t_max < -2 * opts["tol_eig"]: # negative upper bound - status = "NEG_UB" elif n_iter >= opts["max_iter"]: # max iterations status = "MAX_ITER" # plot_along_grad(Q, A_vec, x_new, grad_info["subgrad"], 1) - # Statistics - gap = t_max - t_min - delta_norm = la.norm(delta_x) + # Store data info = dict( n_iter=n_iter, delta_norm=delta_norm, x=x_curr, min_eig_curr=grad_info["min_eig"], - t_max=t_max, - t_min=t_min, + eig_model=eig_model, gap=gap, mult=grad_info["t"], ) @@ -785,14 +807,14 @@ def solve_eopt_sbm( if n_iter % 10 == 0: header_printed = False if header_printed is False: - print(" N | delta_nrm | eig val | t_max |", end="") - print(" t_min | gap | mult. |") + print(" N | delta_nrm | eig val | eig.mdl |", end="") + print(" gap | mult. |") header_printed = True print( - f" {n_iter:3d} | {delta_norm:5.4e} | {grad_info['min_eig']:5.4e} | {t_max:5.4e} |", + f" {n_iter:3d} | {delta_norm:5.4e} | {grad_info['min_eig']:5.4e} | {eig_model:5.4e} |", end="", ) - print(f"{t_min:5.4e} | {gap:5.4e} | {grad_info['t']:4d}") + print(f" {gap:5.4e} | {grad_info['t']:4d}") # Update Iterations n_iter += 1 return x_curr, dict( @@ -800,8 +822,7 @@ def solve_eopt_sbm( H=H, status=status, gap=gap, - t_min=t_min, - t_max=t_max, + model=m, iter_info=pd.DataFrame(iter_info), ) From 5ba1207702efc824b35815d3ead9e7357e795a34 Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Fri, 3 Nov 2023 16:22:59 -0400 Subject: [PATCH 03/19] Removed upper bound logic (doesn't work). Modified constraint eval function to make it faster. --- cert_tools/eopt_solvers.py | 81 ++++++++++++++++++++++++++++++-------- 1 file changed, 64 insertions(+), 17 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 074d7ea..5d6a239 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -649,14 +649,21 @@ def __init__(m, Q, A_vec, V_init, opts=opts_sbm_dflt): m.X = V_init @ V_init.T def eval_A_X(m, V): - A_X_list = [] - for i in range(m.n_vars): - A = m.A_vec[:, i].reshape((m.n_x, m.n_x), order="F") - if V.shape[0] == V.shape[1]: - A_X_list += [np.trace(A @ V)] - else: - A_X_list += [V.T @ A @ V] - return np.vstack(A_X_list) + """computes trace(A_i @ V) for each constraint""" + if not V.shape[0] == V.shape[1]: + X = V @ V.T + else: + X = V + vec_X = X.reshape((-1, 1), order="F") + # A_X_list = [] + # for i in range(m.n_vars): + # A = m.A_vec[:, i].reshape((m.n_x, m.n_x), order="F") + # if V.shape[0] == V.shape[1]: + # A_X_list += [np.trace(A @ V)] + # else: + # A_X_list += [V.T @ A @ V] + + return m.A_vec.T @ vec_X def update_vars(m, opt_info, x_prev, grad_info): """update aggregate matrix variables""" @@ -674,6 +681,41 @@ def update_vars(m, opt_info, x_prev, grad_info): x = x_prev + m.A_X / m.opts["rho_pen"] return x + def get_ub(m, grad_info): + """Compute upper bound of current model""" + if m.opts["r_c"] == 1 and m.opts["r_p"] == 0: + # For simplified problem, UB problem is an LP + # Inequalities + # Set bounds on t level only + bounds = [(0.0, None), (0.0, None)] + A_ineq = np.array([[1.0, 1.0]]) + b_ineq = 1.0 + # Equalities ( A(X) = 0 ) + A_eq = np.hstack([m.A_X, m.eval_A_X(grad_info["min_vec"])]) + b_eq = np.zeros(A_eq.shape[0]) + A_eq = A_eq[[0], :] + b_eq = 0.0 + # Cost + Q_v = grad_info["min_vec"].T @ m.Q @ grad_info["min_vec"] + c = np.array([m.Q_X, Q_v]) + # Run Linprog + res = linprog( + c=c.squeeze(), + A_eq=A_eq, + b_eq=b_eq, + A_ub=A_ineq, + b_ub=b_ineq, + method="highs-ds", + bounds=bounds, + ) + if res.success: + return res.fun + else: + raise ValueError("UB linear subproblem failed.") + return + else: + raise NotImplementedError + def solve_sbm_qp(m, x_curr, grad_info): """Solve Spectral Bundle method subproblem for the case where the SDP variable is scalar.""" @@ -737,6 +779,7 @@ def solve_eopt_sbm( iter_info = [] grad_info = None m = None + min_eig_prev = -np.inf while status == "RUNNING": # SOLVE SPECTRAL BUNDLE PROGRAM if n_iter > 0: @@ -752,7 +795,7 @@ def solve_eopt_sbm( # Compute change in multipliers delta_x = x_curr - x_prev delta_norm = la.norm(delta_x) - # update model upper bound + # Current model value eig_model = ( opt_info["obj_val"][0, 0] + delta_norm**2 * opts["rho_pen"] / 2 ) @@ -760,30 +803,34 @@ def solve_eopt_sbm( # Init step delta_norm = 0.0 eig_model = np.inf + x_prev = x_curr + # GET CERTIFICATE AND GRADIENT INFO # Construct Current Certificate matrix H = get_cert_mat(Q, A_vec, x_curr) # Update gradient and eigenvalue - if n_iter > 0: - min_eig_prev = grad_info["min_eig"] - else: - min_eig_prev = -np.inf grad_info = get_grad_info(H=H, A_vec=A_vec, **kwargs_eig) # Initialize model if m is None: m = SpectralBundleModel(Q, A_vec, grad_info["min_vec"], opts=opts) + # CHECKS + if opts["debug"]: + assert eig_model >= grad_info["min_eig"] - opts["tol_eig"], Exception( + "Model value is below actual." + ) + # STATUS AND VAR UPDATE # Compute the gap gap = eig_model - grad_info["min_eig"] # Serious or Null Step - if grad_info["min_eig"] < min_eig_prev + opts["ser_step_mult"] * gap: + if grad_info["min_eig"] >= min_eig_prev + opts["ser_step_mult"] * gap: + min_eig_prev = grad_info["min_eig"] + else: # Null Step x_curr = x_prev delta_norm = 0.0 # termination criteria if grad_info["min_eig"] >= -opts["tol_eig"]: # positive lower bound status = "POS_LB" - elif eig_model < -5 * opts["tol_eig"]: # ****** EXPERIMENTAL ******* - status = "NEG_UB" elif gap < opts["tol_gap"]: # converged eigenvalue and not positive status = "NEG_UB" elif m.n_vars == 0: # no variables (i.e. no redundant constraints) @@ -807,7 +854,7 @@ def solve_eopt_sbm( if n_iter % 10 == 0: header_printed = False if header_printed is False: - print(" N | delta_nrm | eig val | eig.mdl |", end="") + print(" N | delta_nrm | eig val | mdl opt |", end="") print(" gap | mult. |") header_printed = True print( From 0ef5b72ff8cdb1fb9de5b3b777bd21cc73e50b12 Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Fri, 3 Nov 2023 18:51:13 -0400 Subject: [PATCH 04/19] Intial commit of SDP version of SBM. --- _test/test_eopt_solvers.py | 25 +++++++++++++------------ 1 file changed, 13 insertions(+), 12 deletions(-) diff --git a/_test/test_eopt_solvers.py b/_test/test_eopt_solvers.py index 28b1436..c588e55 100644 --- a/_test/test_eopt_solvers.py +++ b/_test/test_eopt_solvers.py @@ -277,16 +277,16 @@ def test_polynomials(): def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): from cert_tools.eopt_solvers import opts_cut_dflt, opts_sub_dflt, opts_sbm_dflt - print(f"======={prob_file} -- cutting plane ==========") - opts_cut_dflt.update(opts) - run_eopt( - prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" - ) - print(f"======={prob_file} -- subgradient ==========") - opts_sub_dflt.update(opts) - run_eopt( - prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" - ) + # print(f"======={prob_file} -- cutting plane ==========") + # opts_cut_dflt.update(opts) + # run_eopt( + # prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" + # ) + # print(f"======={prob_file} -- subgradient ==========") + # opts_sub_dflt.update(opts) + # run_eopt( + # prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" + # ) print(f"======={prob_file} -- spectral bundle ==========") opts_sbm_dflt.update(opts) run_eopt( @@ -298,7 +298,7 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): import pytest import sys - sys.exit(pytest.main([__file__, "-s"])) + # sys.exit(pytest.main([__file__, "-s"])) # GRADIENT TESTS # test_subgradient_analytic() @@ -306,5 +306,6 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): # test on a new polynomial's globoal minimum # test_rangeonly() - # test_polynomials() + test_polynomials() # test_mw_localize() + # test_eopt(prob_file="test_prob_6.pkl", global_min=False) From a99e511d70bdae434e073c026642dd26274731c9 Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Sun, 5 Nov 2023 18:27:47 -0500 Subject: [PATCH 05/19] SDP version of SBM passing all unit tests. Improved termination criteria on model-actual eig relative gap. --- cert_tools/eopt_solvers.py | 174 ++++++++++++++++++++++++++++--------- 1 file changed, 131 insertions(+), 43 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 5d6a239..8a062ab 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -50,15 +50,15 @@ # Options for Spectral Bundle Method opts_sbm_dflt = dict( tol_eig=1e-6, # Eigenvalue tolerance - tol_gap=1e-7, # gap between model and actual eigenvalue for convergence + tol_gap=5e-4, # term tolerance on relative gap btwn model eig and best eig max_iter=1000, # Maximum iterations tol_null=1e-5, # null space tolerance for first order KKT constraints use_null=True, # if true, reparameterize problem using null space - rho_pen=1e-2, # penalty parameter to ensure closeness to trust region. + rho_pen=1e-3, # penalty parameter to ensure closeness to trust region. ser_step_mult=0.0, # multiplier for "serious step" - r_c=1, # Number of current eigenvectors to keep + r_c=4, # Number of current eigenvectors to keep r_p=0, # Number of previous eigenvectors to keep - debug=True, # Debugging flag + debug=False, # Debugging flag ) @@ -206,6 +206,7 @@ def get_grad_info(H, A_vec, U=None, tau=1e-8, get_hessian=False, **kwargs_eig): # split eigenvector sets based on closeness to min (multiplicity could be > 1) ind_1 = np.abs(eig_vals - min_eig) < tau Q_1 = eig_vecs[:, ind_1] + # Size of matrix n = H.shape[0] # Multiplicity @@ -241,6 +242,7 @@ def get_grad_info(H, A_vec, U=None, tau=1e-8, get_hessian=False, **kwargs_eig): min_vec=Q_1, t=t, damp=damp, + eig_vecs=eig_vecs, ) return grad_info @@ -324,7 +326,7 @@ def solve_eopt( # INITIALIZE # Initialize multiplier variables - x_bar = la.lstsq(A_eq, b_eq, rcond=None)[0] + x_bar = la.lstsq(A_eq, b_eq, rcond=opts["tol_null"])[0] if use_null: # Update Q matrix to include the fixed lagrange multipliers @@ -622,12 +624,16 @@ def solve_eopt_cuts( class SpectralBundleModel: """SpectralBundleModel class stores all of the information associated with the spectral bundle method for eigenvalue optimization. It also stores methods for updating these variables.""" - def __init__(m, Q, A_vec, V_init, opts=opts_sbm_dflt): + def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): # Check that the null space has been removed if not opts["use_null"]: raise ValueError( "Spectral Bundle method requires that the eigenvalue problem is unconstrained. Please preprocess to remove constraints." ) + # Get sizes + r_p = opts["r_p"] + r_c = opts["r_c"] + r_bar = r_p + r_c # Store shape m.n_vars = A_vec.shape[1] m.n_x = Q.shape[0] @@ -635,18 +641,18 @@ def __init__(m, Q, A_vec, V_init, opts=opts_sbm_dflt): m.Q = Q m.A_vec = A_vec # Define the eigenvector matrix - m.V = V_init + m.V = grad_info["eig_vecs"][:, :r_c] # Store Options m.opts = opts if m.n_vars > 0: # Define aggregate matrix variables # TODO: This needs to be changed for the case of r_bar > 1 - m.A_X = m.eval_A_X(V_init) - m.Q_X = V_init.T @ Q @ V_init + m.A_X = m.eval_A_X(m.V) + m.Q_X = np.sum(np.trace(m.V.T @ Q @ m.V)) / r_bar # Debug variables if opts["debug"]: - # Store actual X - m.X = V_init @ V_init.T + # Store actual X (keep unit trace) + m.X = m.V @ m.V.T / r_bar def eval_A_X(m, V): """computes trace(A_i @ V) for each constraint""" @@ -655,30 +661,58 @@ def eval_A_X(m, V): else: X = V vec_X = X.reshape((-1, 1), order="F") - # A_X_list = [] - # for i in range(m.n_vars): - # A = m.A_vec[:, i].reshape((m.n_x, m.n_x), order="F") - # if V.shape[0] == V.shape[1]: - # A_X_list += [np.trace(A @ V)] - # else: - # A_X_list += [V.T @ A @ V] return m.A_vec.T @ vec_X + def update_subspace(m, grad_info): + """populate the subspace vectors with eigenvector information of current + certificate matrix + """ + if m.opts["r_p"] == 0: + m.V = grad_info["eig_vecs"][:, : m.opts["r_c"]] + else: + raise NotImplementedError + def update_vars(m, opt_info, x_prev, grad_info): """update aggregate matrix variables""" - # TODO: Currently only implemented for scalar 'u' variable - # Get optimization information - u = opt_info["u"] - eta = opt_info["eta"] - # Store big X if debugging - if m.opts["debug"]: - m.X = eta * m.X + u * grad_info["min_vec"] @ grad_info["min_vec"].T - # Update agreggate variables - m.A_X = eta * m.A_X + u * grad_info["subgrad"] - m.Q_X = eta * m.Q_X + u * grad_info["min_vec"].T @ m.Q @ grad_info["min_vec"] - # Update null space multipliers (simplified because agg X is optimal X) - x = x_prev + m.A_X / m.opts["rho_pen"] + if m.opts["r_c"] == 1 and m.opts["r_p"] == 0: + # Get optimization information + u = opt_info["u"] + eta = opt_info["eta"] + # Store big X if debugging + if m.opts["debug"]: + m.X = eta * m.X + u * grad_info["min_vec"] @ grad_info["min_vec"].T + # Update agreggate variables + m.A_X = eta * m.A_X + u * grad_info["subgrad"] + m.Q_X = ( + eta * m.Q_X + u * grad_info["min_vec"].T @ m.Q @ grad_info["min_vec"] + ) + # Update null space multipliers (simplified because agg X is optimal X) + x = x_prev + m.A_X / m.opts["rho_pen"] + elif m.opts["r_c"] > 1 and m.opts["r_p"] == 0: + # Get optimization information + U = opt_info["U"] + eta = opt_info["eta"] + # Store big X if debugging + if m.opts["debug"]: + m.X = eta * m.X + m.V @ U @ m.V.T + assert np.trace(m.X) < 1 + 1e-7 + # Update agreggate variables + m.A_X = opt_info["A_X"] + VQV = m.V.T @ m.Q @ m.V + m.Q_X = eta * m.Q_X + np.trace(VQV @ U) + # DEBUG assert that the A_X and Q_X are correct + if m.opts["debug"]: + np.testing.assert_almost_equal( + m.A_X, m.eval_A_X(m.X), err_msg="A_X not correct" + ) + np.testing.assert_almost_equal( + m.Q_X, np.trace(m.Q @ m.X), err_msg="Q_X not correct" + ) + # Update null space multipliers (simplified because agg X is optimal X) + x = x_prev + opt_info["A_X"] / m.opts["rho_pen"] + else: + raise NotImplementedError return x def get_ub(m, grad_info): @@ -748,6 +782,49 @@ def solve_sbm_qp(m, x_curr, grad_info): ) return opt_info + def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): + """Solve the spectral bundle method SDP subproblem to find optimal multiplier + update. This function should only be called if r_p + r_c = r_bar > 1 + + Args: + m (_type_): _description_ + x_curr (_type_): _description_ + H_curr (_type_): _description_ + grad_info (_type_): _description_ + verbose (bool, optional): _description_. Defaults to False. + + Returns: + _type_: _description_ + """ + # Define Variables + r_bar = m.opts["r_p"] + m.opts["r_c"] + U = cp.Variable((r_bar, r_bar), symmetric=True) + eta = cp.Variable() + # Constraints + constraints = [U >> 0] + constraints += [eta >= 0] + constraints += [eta + cp.trace(U) <= 1] + # Objective + obj = eta * (m.Q_X + m.A_X.T @ x_curr) + obj += cp.trace((m.V.T @ H_curr @ m.V) @ U) + + A_VUV = (m.A_vec.T @ np.kron(m.V, m.V)) @ ( + cp.reshape(U, (r_bar**2, 1), order="F") + ) + A_X = eta * m.A_X + A_VUV + obj += 1 / 2 / m.opts["rho_pen"] * cp.sum_squares(A_X) + # Define the SDP + cprob = cp.Problem(cp.Minimize(obj), constraints) + sdp_opts = dict(verbose=m.opts["debug"]) + # Solve the SDP + cprob.solve( + solver="MOSEK", + **sdp_opts, + ) + # Return opt data + opt_info = dict(U=U.value, eta=eta.value, obj_val=obj.value, A_X=A_X.value) + return opt_info + def solve_eopt_sbm( Q, @@ -771,6 +848,9 @@ def solve_eopt_sbm( opts (_type_, optional): _description_. Defaults to opts_cut_dflt. kwargs_eig (dict, optional): _description_. Defaults to {}. """ + # Update required number of eigenvalues + n_eigs = np.min([opts["r_c"], Q.shape[0]]) + kwargs_eig.update(k=n_eigs) # Intialize status vars for optimization status = "RUNNING" header_printed = False @@ -779,14 +859,14 @@ def solve_eopt_sbm( iter_info = [] grad_info = None m = None - min_eig_prev = -np.inf + min_eig_best = -np.inf while status == "RUNNING": # SOLVE SPECTRAL BUNDLE PROGRAM if n_iter > 0: if opts["r_c"] == 1 and opts["r_p"] == 0: opt_info = m.solve_sbm_qp(x_curr=x_curr, grad_info=grad_info) else: - raise NotImplementedError + opt_info = m.solve_sbm_sdp(x_curr=x_curr, H_curr=H, grad_info=grad_info) # Update variables x_prev = x_curr.copy() x_curr = m.update_vars( @@ -810,9 +890,11 @@ def solve_eopt_sbm( H = get_cert_mat(Q, A_vec, x_curr) # Update gradient and eigenvalue grad_info = get_grad_info(H=H, A_vec=A_vec, **kwargs_eig) - # Initialize model + # Update model with gradient information if m is None: - m = SpectralBundleModel(Q, A_vec, grad_info["min_vec"], opts=opts) + m = SpectralBundleModel(Q, A_vec, grad_info, opts=opts) + else: + m.update_subspace(grad_info) # CHECKS if opts["debug"]: assert eig_model >= grad_info["min_eig"] - opts["tol_eig"], Exception( @@ -821,18 +903,22 @@ def solve_eopt_sbm( # STATUS AND VAR UPDATE # Compute the gap - gap = eig_model - grad_info["min_eig"] + gap = eig_model - min_eig_best + gap_rel = gap / np.abs(min_eig_best) # Serious or Null Step - if grad_info["min_eig"] >= min_eig_prev + opts["ser_step_mult"] * gap: - min_eig_prev = grad_info["min_eig"] + if ( + grad_info["min_eig"] >= min_eig_best + opts["ser_step_mult"] * gap + or n_iter == 0 + ): + min_eig_best = grad_info["min_eig"] else: # Null Step x_curr = x_prev delta_norm = 0.0 # termination criteria if grad_info["min_eig"] >= -opts["tol_eig"]: # positive lower bound status = "POS_LB" - elif gap < opts["tol_gap"]: # converged eigenvalue and not positive - status = "NEG_UB" + elif gap_rel < opts["tol_gap"]: # converged eigenvalue and not positive + status = "GAP" elif m.n_vars == 0: # no variables (i.e. no redundant constraints) status = "NO_VAR" elif n_iter >= opts["max_iter"]: # max iterations @@ -854,14 +940,16 @@ def solve_eopt_sbm( if n_iter % 10 == 0: header_printed = False if header_printed is False: - print(" N | delta_nrm | eig val | mdl opt |", end="") - print(" gap | mult. |") + print( + " N | delta_nrm | eig val | eig bst | mdl opt |", end="" + ) + print(" rel gap | mult. |") header_printed = True print( - f" {n_iter:3d} | {delta_norm:5.4e} | {grad_info['min_eig']:5.4e} | {eig_model:5.4e} |", + f" {n_iter:3d} | {delta_norm:5.4e} | {grad_info['min_eig']:5.4e} | {min_eig_best:5.4e} | {eig_model:5.4e} |", end="", ) - print(f" {gap:5.4e} | {grad_info['t']:4d}") + print(f" {gap_rel:5.4e} | {grad_info['t']:4d}") # Update Iterations n_iter += 1 return x_curr, dict( From b41543ff576992424726f40e648ce61f6ebc8ef9 Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Mon, 6 Nov 2023 15:57:31 -0500 Subject: [PATCH 06/19] some linting. Removed 79 char requirement for flake8. --- cert_tools/eopt_solvers.py | 1 + setup.cfg | 2 +- 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 8a062ab..c277f4c 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -860,6 +860,7 @@ def solve_eopt_sbm( grad_info = None m = None min_eig_best = -np.inf + H = None while status == "RUNNING": # SOLVE SPECTRAL BUNDLE PROGRAM if n_iter > 0: diff --git a/setup.cfg b/setup.cfg index 98f371c..e77f682 100644 --- a/setup.cfg +++ b/setup.cfg @@ -27,6 +27,6 @@ install_requires = exclude=_test* [flake8] -ignore = W292, W391, F541, F841, +ignore = W292, W391, F541, F841, E501, exclude = _notebooks/*, *.ipynb_checkpoints* max-line-length = 99 From ca93fb03a47e2aa5228560ed584bc5b6b07cfe76 Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Mon, 6 Nov 2023 16:17:38 -0500 Subject: [PATCH 07/19] fixed accidental test file changes. added cvxopt as backup for mosek --- _test/test_eopt_solvers.py | 25 ++++++++++++------------- cert_tools/eopt_solvers.py | 12 +++++++----- 2 files changed, 19 insertions(+), 18 deletions(-) diff --git a/_test/test_eopt_solvers.py b/_test/test_eopt_solvers.py index c588e55..28b1436 100644 --- a/_test/test_eopt_solvers.py +++ b/_test/test_eopt_solvers.py @@ -277,16 +277,16 @@ def test_polynomials(): def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): from cert_tools.eopt_solvers import opts_cut_dflt, opts_sub_dflt, opts_sbm_dflt - # print(f"======={prob_file} -- cutting plane ==========") - # opts_cut_dflt.update(opts) - # run_eopt( - # prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" - # ) - # print(f"======={prob_file} -- subgradient ==========") - # opts_sub_dflt.update(opts) - # run_eopt( - # prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" - # ) + print(f"======={prob_file} -- cutting plane ==========") + opts_cut_dflt.update(opts) + run_eopt( + prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" + ) + print(f"======={prob_file} -- subgradient ==========") + opts_sub_dflt.update(opts) + run_eopt( + prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" + ) print(f"======={prob_file} -- spectral bundle ==========") opts_sbm_dflt.update(opts) run_eopt( @@ -298,7 +298,7 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): import pytest import sys - # sys.exit(pytest.main([__file__, "-s"])) + sys.exit(pytest.main([__file__, "-s"])) # GRADIENT TESTS # test_subgradient_analytic() @@ -306,6 +306,5 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): # test on a new polynomial's globoal minimum # test_rangeonly() - test_polynomials() + # test_polynomials() # test_mw_localize() - # test_eopt(prob_file="test_prob_6.pkl", global_min=False) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index c277f4c..2e18a3c 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -814,13 +814,15 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): A_X = eta * m.A_X + A_VUV obj += 1 / 2 / m.opts["rho_pen"] * cp.sum_squares(A_X) # Define the SDP - cprob = cp.Problem(cp.Minimize(obj), constraints) + prob = cp.Problem(cp.Minimize(obj), constraints) sdp_opts = dict(verbose=m.opts["debug"]) # Solve the SDP - cprob.solve( - solver="MOSEK", - **sdp_opts, - ) + try: + prob.solve(solver="MOSEK", **sdp_opts) + except mosek.Error: + print("Did not find MOSEK, using different solver.") + prob.solve(solver="CVXOPT", **sdp_opts) + # Return opt data opt_info = dict(U=U.value, eta=eta.value, obj_val=obj.value, A_X=A_X.value) return opt_info From b8babf5526d3b44139904fe616b7142f65b70d5e Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Fri, 3 Nov 2023 18:51:13 -0400 Subject: [PATCH 08/19] Intial commit of SDP version of SBM. --- _test/test_eopt_solvers.py | 25 +++++++++++++------------ 1 file changed, 13 insertions(+), 12 deletions(-) diff --git a/_test/test_eopt_solvers.py b/_test/test_eopt_solvers.py index 28b1436..c588e55 100644 --- a/_test/test_eopt_solvers.py +++ b/_test/test_eopt_solvers.py @@ -277,16 +277,16 @@ def test_polynomials(): def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): from cert_tools.eopt_solvers import opts_cut_dflt, opts_sub_dflt, opts_sbm_dflt - print(f"======={prob_file} -- cutting plane ==========") - opts_cut_dflt.update(opts) - run_eopt( - prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" - ) - print(f"======={prob_file} -- subgradient ==========") - opts_sub_dflt.update(opts) - run_eopt( - prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" - ) + # print(f"======={prob_file} -- cutting plane ==========") + # opts_cut_dflt.update(opts) + # run_eopt( + # prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" + # ) + # print(f"======={prob_file} -- subgradient ==========") + # opts_sub_dflt.update(opts) + # run_eopt( + # prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" + # ) print(f"======={prob_file} -- spectral bundle ==========") opts_sbm_dflt.update(opts) run_eopt( @@ -298,7 +298,7 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): import pytest import sys - sys.exit(pytest.main([__file__, "-s"])) + # sys.exit(pytest.main([__file__, "-s"])) # GRADIENT TESTS # test_subgradient_analytic() @@ -306,5 +306,6 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): # test on a new polynomial's globoal minimum # test_rangeonly() - # test_polynomials() + test_polynomials() # test_mw_localize() + # test_eopt(prob_file="test_prob_6.pkl", global_min=False) From ec3c39628cfda45ebb7b0de22e152c4488b8d7cf Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Mon, 6 Nov 2023 16:17:38 -0500 Subject: [PATCH 09/19] fixed accidental test file changes. added cvxopt as backup for mosek --- _test/test_eopt_solvers.py | 25 ++++++++++++------------- 1 file changed, 12 insertions(+), 13 deletions(-) diff --git a/_test/test_eopt_solvers.py b/_test/test_eopt_solvers.py index c588e55..28b1436 100644 --- a/_test/test_eopt_solvers.py +++ b/_test/test_eopt_solvers.py @@ -277,16 +277,16 @@ def test_polynomials(): def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): from cert_tools.eopt_solvers import opts_cut_dflt, opts_sub_dflt, opts_sbm_dflt - # print(f"======={prob_file} -- cutting plane ==========") - # opts_cut_dflt.update(opts) - # run_eopt( - # prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" - # ) - # print(f"======={prob_file} -- subgradient ==========") - # opts_sub_dflt.update(opts) - # run_eopt( - # prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" - # ) + print(f"======={prob_file} -- cutting plane ==========") + opts_cut_dflt.update(opts) + run_eopt( + prob_file=prob_file, opts=opts_cut_dflt, global_min=global_min, method="cuts" + ) + print(f"======={prob_file} -- subgradient ==========") + opts_sub_dflt.update(opts) + run_eopt( + prob_file=prob_file, opts=opts_sub_dflt, global_min=global_min, method="sub" + ) print(f"======={prob_file} -- spectral bundle ==========") opts_sbm_dflt.update(opts) run_eopt( @@ -298,7 +298,7 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): import pytest import sys - # sys.exit(pytest.main([__file__, "-s"])) + sys.exit(pytest.main([__file__, "-s"])) # GRADIENT TESTS # test_subgradient_analytic() @@ -306,6 +306,5 @@ def test_eopt(prob_file="test_prob_4.pkl", global_min=True, opts={}): # test on a new polynomial's globoal minimum # test_rangeonly() - test_polynomials() + # test_polynomials() # test_mw_localize() - # test_eopt(prob_file="test_prob_6.pkl", global_min=False) From 664c97fc6001bbe054a10b95706358a4a3170d6e Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Mon, 6 Nov 2023 19:45:18 -0500 Subject: [PATCH 10/19] defined trust region agreement variable and changed null step criteria accordingly. --- cert_tools/eopt_solvers.py | 42 ++++++++++++++++++++------------------ 1 file changed, 22 insertions(+), 20 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 2e18a3c..50e0f8d 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -55,7 +55,7 @@ tol_null=1e-5, # null space tolerance for first order KKT constraints use_null=True, # if true, reparameterize problem using null space rho_pen=1e-3, # penalty parameter to ensure closeness to trust region. - ser_step_mult=0.0, # multiplier for "serious step" + agreement_req=0.0, # multiplier for "serious step" r_c=4, # Number of current eigenvectors to keep r_p=0, # Number of previous eigenvectors to keep debug=False, # Debugging flag @@ -630,6 +630,10 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): raise ValueError( "Spectral Bundle method requires that the eigenvalue problem is unconstrained. Please preprocess to remove constraints." ) + # Store Options + m.opts = opts + # Initialize the trust region penalty parameter + m.rho_pen = opts["rho_pen"] # Get sizes r_p = opts["r_p"] r_c = opts["r_c"] @@ -642,8 +646,7 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): m.A_vec = A_vec # Define the eigenvector matrix m.V = grad_info["eig_vecs"][:, :r_c] - # Store Options - m.opts = opts + if m.n_vars > 0: # Define aggregate matrix variables # TODO: This needs to be changed for the case of r_bar > 1 @@ -687,8 +690,7 @@ def update_vars(m, opt_info, x_prev, grad_info): m.Q_X = ( eta * m.Q_X + u * grad_info["min_vec"].T @ m.Q @ grad_info["min_vec"] ) - # Update null space multipliers (simplified because agg X is optimal X) - x = x_prev + m.A_X / m.opts["rho_pen"] + elif m.opts["r_c"] > 1 and m.opts["r_p"] == 0: # Get optimization information U = opt_info["U"] @@ -709,10 +711,12 @@ def update_vars(m, opt_info, x_prev, grad_info): np.testing.assert_almost_equal( m.Q_X, np.trace(m.Q @ m.X), err_msg="Q_X not correct" ) - # Update null space multipliers (simplified because agg X is optimal X) - x = x_prev + opt_info["A_X"] / m.opts["rho_pen"] else: raise NotImplementedError + # Update multipliers + x = x_prev + m.A_X / m.rho_pen + # TODO Implement the null step checks here. + return x def get_ub(m, grad_info): @@ -763,9 +767,7 @@ def solve_sbm_qp(m, x_curr, grad_info): obj = ( eta * (m.Q_X + m.A_X.T @ x_curr) + u * grad_info["min_eig"] - + cp.sum_squares(eta * m.A_X + u * grad_info["subgrad"]) - / 2 - / m.opts["rho_pen"] + + cp.sum_squares(eta * m.A_X + u * grad_info["subgrad"]) / 2 / m.rho_pen ) # Solve Quadratic Program: prob = cp.Problem(cp.Minimize(obj), constraints) @@ -812,7 +814,7 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): cp.reshape(U, (r_bar**2, 1), order="F") ) A_X = eta * m.A_X + A_VUV - obj += 1 / 2 / m.opts["rho_pen"] * cp.sum_squares(A_X) + obj += 1 / 2 / m.rho_pen * cp.sum_squares(A_X) # Define the SDP prob = cp.Problem(cp.Minimize(obj), constraints) sdp_opts = dict(verbose=m.opts["debug"]) @@ -879,9 +881,7 @@ def solve_eopt_sbm( delta_x = x_curr - x_prev delta_norm = la.norm(delta_x) # Current model value - eig_model = ( - opt_info["obj_val"][0, 0] + delta_norm**2 * opts["rho_pen"] / 2 - ) + eig_model = opt_info["obj_val"][0, 0] + delta_norm**2 * m.rho_pen / 2 else: # Init step delta_norm = 0.0 @@ -908,13 +908,15 @@ def solve_eopt_sbm( # Compute the gap gap = eig_model - min_eig_best gap_rel = gap / np.abs(min_eig_best) - # Serious or Null Step - if ( - grad_info["min_eig"] >= min_eig_best + opts["ser_step_mult"] * gap - or n_iter == 0 - ): + # Compute the model-objective agreement + delta_predict = eig_model - min_eig_best + delta_actual = grad_info["min_eig"] - min_eig_best + rho_agree = delta_actual / delta_predict + + # Check if model-objective agreement is acceptable + if rho_agree >= opts["agreement_req"] or n_iter == 0: min_eig_best = grad_info["min_eig"] - else: # Null Step + else: # If model agreement is bad then don't step x_curr = x_prev delta_norm = 0.0 # termination criteria From 1feaf26403a23a1a3a88de9962408c3ad223649e Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Tue, 7 Nov 2023 13:55:45 -0500 Subject: [PATCH 11/19] Variable trust region implemented cd /home/cho/research/mat_weight_certs ; /usr/bin/env /home/cho/mambaforge/envs/mwcerts/bin/python /home/cho/.vscode-server/extensions/ms-python.python-2023.20.0/pythonFiles/lib/python/debugpy/adapter/../../debugpy/launcher 56175 -- /home/cho/research/mat_weight_certs/src/certifiable-tools/_script/explore_prob_6.py --- cert_tools/eopt_solvers.py | 63 ++++++++++++++++++++++++++++---------- cert_tools/sdp_solvers.py | 24 +++++---------- 2 files changed, 55 insertions(+), 32 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 50e0f8d..d18c49f 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -54,7 +54,7 @@ max_iter=1000, # Maximum iterations tol_null=1e-5, # null space tolerance for first order KKT constraints use_null=True, # if true, reparameterize problem using null space - rho_pen=1e-3, # penalty parameter to ensure closeness to trust region. + trust_reg=1e2, # Initial trust region size agreement_req=0.0, # multiplier for "serious step" r_c=4, # Number of current eigenvectors to keep r_p=0, # Number of previous eigenvectors to keep @@ -632,8 +632,6 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): ) # Store Options m.opts = opts - # Initialize the trust region penalty parameter - m.rho_pen = opts["rho_pen"] # Get sizes r_p = opts["r_p"] r_c = opts["r_c"] @@ -646,7 +644,9 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): m.A_vec = A_vec # Define the eigenvector matrix m.V = grad_info["eig_vecs"][:, :r_c] - + # Define trust region + m.trust_reg = opts["trust_reg"] + m.trust_reg_ub = opts["trust_reg"] if m.n_vars > 0: # Define aggregate matrix variables # TODO: This needs to be changed for the case of r_bar > 1 @@ -656,6 +656,12 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): if opts["debug"]: # Store actual X (keep unit trace) m.X = m.V @ m.V.T / r_bar + # Initialize the trust region penalty parameter + + m.penalty = np.linalg.norm(m.A_X) / m.trust_reg + else: + # Random values (Don't matter) + m.penalty = 1.0 def eval_A_X(m, V): """computes trace(A_i @ V) for each constraint""" @@ -714,7 +720,7 @@ def update_vars(m, opt_info, x_prev, grad_info): else: raise NotImplementedError # Update multipliers - x = x_prev + m.A_X / m.rho_pen + x = x_prev + m.A_X / m.penalty # TODO Implement the null step checks here. return x @@ -767,7 +773,7 @@ def solve_sbm_qp(m, x_curr, grad_info): obj = ( eta * (m.Q_X + m.A_X.T @ x_curr) + u * grad_info["min_eig"] - + cp.sum_squares(eta * m.A_X + u * grad_info["subgrad"]) / 2 / m.rho_pen + + cp.sum_squares(eta * m.A_X + u * grad_info["subgrad"]) / 2 / m.penalty ) # Solve Quadratic Program: prob = cp.Problem(cp.Minimize(obj), constraints) @@ -814,7 +820,7 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): cp.reshape(U, (r_bar**2, 1), order="F") ) A_X = eta * m.A_X + A_VUV - obj += 1 / 2 / m.rho_pen * cp.sum_squares(A_X) + obj += 1 / 2 / m.penalty * cp.sum_squares(A_X) # Define the SDP prob = cp.Problem(cp.Minimize(obj), constraints) sdp_opts = dict(verbose=m.opts["debug"]) @@ -829,6 +835,32 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): opt_info = dict(U=U.value, eta=eta.value, obj_val=obj.value, A_X=A_X.value) return opt_info + def update_trust(m, rho, delta_norm): + """Update the effective trust region for SBM. Note that the trust region is + currently maintained by adapting the penalty term, since the SBM uses a + a penalty. + + Args: + m (_type_): _description_ + rho (_type_): _description_ + """ + if m.n_vars > 0: + A_X_norm = np.linalg.norm(m.A_X) + else: + A_X_norm = 1.0 + # Perform trust region update (See Nocedal and Wright) + if rho < 1 / 4: + # Shrink trust region + m.trust_reg = m.trust_reg / 4 + else: + # Expand trust region + trust_reg_num = A_X_norm / m.penalty + if rho > 3 / 4 and delta_norm - trust_reg_num >= -1e-10: + m.trust_reg = min(2 * m.trust_reg, m.trust_reg_ub) + # Otherwise keep same region + # Update the penalty + m.penalty = np.max([A_X_norm / m.trust_reg, 1.0e-8]) + def solve_eopt_sbm( Q, @@ -881,7 +913,7 @@ def solve_eopt_sbm( delta_x = x_curr - x_prev delta_norm = la.norm(delta_x) # Current model value - eig_model = opt_info["obj_val"][0, 0] + delta_norm**2 * m.rho_pen / 2 + eig_model = opt_info["obj_val"][0, 0] + delta_norm**2 * m.penalty / 2 else: # Init step delta_norm = 0.0 @@ -905,14 +937,14 @@ def solve_eopt_sbm( ) # STATUS AND VAR UPDATE - # Compute the gap - gap = eig_model - min_eig_best - gap_rel = gap / np.abs(min_eig_best) # Compute the model-objective agreement delta_predict = eig_model - min_eig_best delta_actual = grad_info["min_eig"] - min_eig_best rho_agree = delta_actual / delta_predict - + # Relative gap between model and actual + gap_rel = delta_actual / np.abs(min_eig_best) + # Update the trust region + m.update_trust(rho_agree, delta_norm) # Check if model-objective agreement is acceptable if rho_agree >= opts["agreement_req"] or n_iter == 0: min_eig_best = grad_info["min_eig"] @@ -937,7 +969,7 @@ def solve_eopt_sbm( x=x_curr, min_eig_curr=grad_info["min_eig"], eig_model=eig_model, - gap=gap, + gap_rel=gap_rel, mult=grad_info["t"], ) iter_info += [info] @@ -948,20 +980,19 @@ def solve_eopt_sbm( print( " N | delta_nrm | eig val | eig bst | mdl opt |", end="" ) - print(" rel gap | mult. |") + print(" rel gap | trust | mult. |") header_printed = True print( f" {n_iter:3d} | {delta_norm:5.4e} | {grad_info['min_eig']:5.4e} | {min_eig_best:5.4e} | {eig_model:5.4e} |", end="", ) - print(f" {gap_rel:5.4e} | {grad_info['t']:4d}") + print(f" {gap_rel:5.4e} | {m.trust_reg:5.4e} | {grad_info['t']:4d}") # Update Iterations n_iter += 1 return x_curr, dict( min_eig=grad_info["min_eig"], H=H, status=status, - gap=gap, model=m, iter_info=pd.DataFrame(iter_info), ) diff --git a/cert_tools/sdp_solvers.py b/cert_tools/sdp_solvers.py index 8b7193e..55cc864 100644 --- a/cert_tools/sdp_solvers.py +++ b/cert_tools/sdp_solvers.py @@ -204,11 +204,12 @@ def streamprinter(text): # Get status information about the solution prosta = task.getprosta(mosek.soltype.itr) solsta = task.getsolsta(mosek.soltype.itr) + X = None + cost = None + yvals = None if solsta == mosek.solsta.optimal: - msg = "Optimal" barx = task.getbarxj(mosek.soltype.itr, 0) cost = task.getprimalobj(mosek.soltype.itr) * scale + offset - yvals = np.array(task.getbarsj(mosek.soltype.itr, 0)) X = np.zeros((dim, dim)) cnt = 0 for i in range(dim): @@ -219,28 +220,19 @@ def streamprinter(text): X[j, i] = barx[cnt] X[i, j] = barx[cnt] cnt += 1 + # Get yvals + yvals = task.getsolution(mosek.soltype.itr)[7] elif ( solsta == mosek.solsta.dual_infeas_cer or solsta == mosek.solsta.prim_infeas_cer ): - msg = "Primal or dual infeasibility certificate found.\n" - X = np.nan - cost = np.nan + print("Primal or dual infeasibility certificate found.\n") elif solsta == mosek.solsta.unknown: - msg = "Unknown solution status" - X = np.nan - cost = np.nan + print("Unknown solution status") else: - msg = f"Other solution status: {solsta}" - X = np.nan - cost = np.nan - - # H = Q_here - LHS.value - # yvals = [x.value for x in y] + print("Other solution status") - # TODO(FD) can we read the dual variables from mosek solution? info = {"H": None, "yvals": yvals, "cost": cost, "msg": msg} - # info = {"cost": cost, "msg": msg} return X, info From c371cdbab01d1ba83e3550ac03fc84bae271261d Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Tue, 7 Nov 2023 14:52:14 -0500 Subject: [PATCH 12/19] redefined parameter inputs in terms of trust region. 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z8-K7#7xQ6^?Bc>_71)IKyffRSvmfuiPtVr1F$aJWJ?`$7l!tgHi>rxC;}C49^-9sJ z225iQ_2^_2BT?SHZAUKRKYIV4UEj$s5bb+&(@WV7;ENS$(3@d^>BIrWz2j7*#Oy3n z=x9Q|`;a%T=cry}?JdP^05n#Q@u4PN6|9UNcLc~Y{L2G(bt zwR9{e0W)FrhK9Dmfp(6T{HZP!;`91^-NA9V@y5Ad58v2if4ePNx|a@|@Nf1n@CjU| zPt1sldohd~bz0Or(UIxekbAlmZmu3b{XR186}WGCNpKxzstRYLioNSi=$L#){R81+_>Sw0Eio%t9K+af#E1)dC?#DvMovzi=-(yx82Wf z^4=%tNM!VsX5MH}m?a_gu7ZHPR@Fl%N>NOPy aK)Wfm!v$|ATZ9*6j^R<+e~)X|RsI8VwsUI$ diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index d18c49f..4acfedc 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -942,7 +942,7 @@ def solve_eopt_sbm( delta_actual = grad_info["min_eig"] - min_eig_best rho_agree = delta_actual / delta_predict # Relative gap between model and actual - gap_rel = delta_actual / np.abs(min_eig_best) + gap_rel = np.abs(delta_actual / min_eig_best) # Update the trust region m.update_trust(rho_agree, delta_norm) # Check if model-objective agreement is acceptable @@ -954,7 +954,9 @@ def solve_eopt_sbm( # termination criteria if grad_info["min_eig"] >= -opts["tol_eig"]: # positive lower bound status = "POS_LB" - elif gap_rel < opts["tol_gap"]: # converged eigenvalue and not positive + elif ( + gap_rel * m.penalty < opts["tol_gap"] + ): # converged eigenvalue and not positive status = "GAP" elif m.n_vars == 0: # no variables (i.e. no redundant constraints) status = "NO_VAR" From 7883579d64664ce66ce5080e9d9e3df8198ac256 Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Thu, 9 Nov 2023 13:57:16 -0500 Subject: [PATCH 13/19] Added lower bound on trust region. --- cert_tools/eopt_solvers.py | 42 +++++++++++++++++++++++--------------- 1 file changed, 25 insertions(+), 17 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 4acfedc..557e902 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -54,10 +54,14 @@ max_iter=1000, # Maximum iterations tol_null=1e-5, # null space tolerance for first order KKT constraints use_null=True, # if true, reparameterize problem using null space - trust_reg=1e2, # Initial trust region size - agreement_req=0.0, # multiplier for "serious step" + trust_reg_adapt=True # Use trust region adaptation + trust_reg_init=1e2, # Initial trust region size + trust_reg_ub=1e3, # Trust Region upper bound + trust_reg_lb=1e-7, # Trust Region lower bound + agreement_req=0.0, # Requirement on model agreement to take a serious step r_c=4, # Number of current eigenvectors to keep r_p=0, # Number of previous eigenvectors to keep + tol_mult_eig = 1e-3 # Tolerance for multiplicity when adapting r_c debug=False, # Debugging flag ) @@ -199,12 +203,12 @@ def f_eopt(Q, A_vec, x, **kwargs_eig): return grad_info["min_eig"] -def get_grad_info(H, A_vec, U=None, tau=1e-8, get_hessian=False, **kwargs_eig): +def get_grad_info(H, A_vec, U=None, tol_mult=1e-8, get_hessian=False, **kwargs_eig): eig_vals, eig_vecs = get_min_eigpairs(H, **kwargs_eig) # get minimum eigenvalue min_eig = np.min(eig_vals) # split eigenvector sets based on closeness to min (multiplicity could be > 1) - ind_1 = np.abs(eig_vals - min_eig) < tau + ind_1 = np.abs(eig_vals - min_eig) < tol_mult Q_1 = eig_vecs[:, ind_1] # Size of matrix @@ -223,7 +227,7 @@ def get_grad_info(H, A_vec, U=None, tau=1e-8, get_hessian=False, **kwargs_eig): # Compute Hessian if t == 1 and get_hessian: # Get other eigvectors and eigenvalues - ind_s = np.abs(eig_vals - min_eig) >= tau + ind_s = np.abs(eig_vals - min_eig) >= tol_mult Q_s = eig_vecs[:, ind_s] eig_inv_diffs = 1 / (min_eig - eig_vals[ind_s]) Lambda_s = np.diag(eig_inv_diffs) @@ -645,8 +649,10 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): # Define the eigenvector matrix m.V = grad_info["eig_vecs"][:, :r_c] # Define trust region - m.trust_reg = opts["trust_reg"] - m.trust_reg_ub = opts["trust_reg"] + m.trust_reg = opts["trust_reg_init"] + m.trust_reg_ub = opts["trust_reg_ub"] + m.trust_reg_lb = opts["trust_reg_lb"] + # Check if opt variables exist if m.n_vars > 0: # Define aggregate matrix variables # TODO: This needs to be changed for the case of r_bar > 1 @@ -657,7 +663,6 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): # Store actual X (keep unit trace) m.X = m.V @ m.V.T / r_bar # Initialize the trust region penalty parameter - m.penalty = np.linalg.norm(m.A_X) / m.trust_reg else: # Random values (Don't matter) @@ -720,9 +725,8 @@ def update_vars(m, opt_info, x_prev, grad_info): else: raise NotImplementedError # Update multipliers + # x = x_prev + m.A_X / np.linalg.norm(m.A_X) * m.trust_reg x = x_prev + m.A_X / m.penalty - # TODO Implement the null step checks here. - return x def get_ub(m, grad_info): @@ -851,15 +855,17 @@ def update_trust(m, rho, delta_norm): # Perform trust region update (See Nocedal and Wright) if rho < 1 / 4: # Shrink trust region - m.trust_reg = m.trust_reg / 4 + m.trust_reg = max(m.trust_reg / 4, m.trust_reg_lb) else: # Expand trust region - trust_reg_num = A_X_norm / m.penalty - if rho > 3 / 4 and delta_norm - trust_reg_num >= -1e-10: + trust_reg_actual = A_X_norm / m.penalty + trust_violation = delta_norm - trust_reg_actual + assert trust_violation < 1e-2, ValueError("Trust Region Violated") + if rho > 3 / 4: m.trust_reg = min(2 * m.trust_reg, m.trust_reg_ub) # Otherwise keep same region # Update the penalty - m.penalty = np.max([A_X_norm / m.trust_reg, 1.0e-8]) + m.penalty = max(A_X_norm / m.trust_reg, 1.0e-8) def solve_eopt_sbm( @@ -944,7 +950,8 @@ def solve_eopt_sbm( # Relative gap between model and actual gap_rel = np.abs(delta_actual / min_eig_best) # Update the trust region - m.update_trust(rho_agree, delta_norm) + if m.opts["trust_reg_adapt"]: + m.update_trust(rho_agree, delta_norm) # Check if model-objective agreement is acceptable if rho_agree >= opts["agreement_req"] or n_iter == 0: min_eig_best = grad_info["min_eig"] @@ -962,7 +969,7 @@ def solve_eopt_sbm( status = "NO_VAR" elif n_iter >= opts["max_iter"]: # max iterations status = "MAX_ITER" - # plot_along_grad(Q, A_vec, x_new, grad_info["subgrad"], 1) + # plot_along_grad(Q, A_vec, x_curr, m.A_X, 1) # Store data info = dict( @@ -973,6 +980,7 @@ def solve_eopt_sbm( eig_model=eig_model, gap_rel=gap_rel, mult=grad_info["t"], + rho_agree=rho_agree, ) iter_info += [info] if verbose: @@ -1025,7 +1033,7 @@ def get_cert_mat(C, A_vec, mults, sparsify=True, exploit_centered=False): def plot_along_grad(C, A_vec, mults, step, alpha_max): - alphas = np.linspace(0, alpha_max, 100) + alphas = np.linspace(-alpha_max, alpha_max, 100) min_eigs = np.zeros(alphas.shape) for i in range(len(alphas)): step_alpha = mults + alphas[i] * step From 0ba7b373d0cb2db71ba4eef9cb6fc4c957d63d3e Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Thu, 9 Nov 2023 14:50:52 -0500 Subject: [PATCH 14/19] Added adaptive eigenspace size, depending on the number of eigenvalues that are close to the current minimum eigenvalue. --- cert_tools/eopt_solvers.py | 34 ++++++++++++++++++++-------------- 1 file changed, 20 insertions(+), 14 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 557e902..051fa74 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -54,14 +54,14 @@ max_iter=1000, # Maximum iterations tol_null=1e-5, # null space tolerance for first order KKT constraints use_null=True, # if true, reparameterize problem using null space - trust_reg_adapt=True # Use trust region adaptation + trust_reg_adapt=True, # Use trust region adaptation trust_reg_init=1e2, # Initial trust region size trust_reg_ub=1e3, # Trust Region upper bound trust_reg_lb=1e-7, # Trust Region lower bound agreement_req=0.0, # Requirement on model agreement to take a serious step - r_c=4, # Number of current eigenvectors to keep + r_c_max=15, # Number of current eigenvectors to keep r_p=0, # Number of previous eigenvectors to keep - tol_mult_eig = 1e-3 # Tolerance for multiplicity when adapting r_c + tol_mult_eig=1e-3, # Tolerance for multiplicity when adapting r_c debug=False, # Debugging flag ) @@ -638,8 +638,8 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): m.opts = opts # Get sizes r_p = opts["r_p"] - r_c = opts["r_c"] - r_bar = r_p + r_c + m.r_c = 1 + r_bar = r_p + m.r_c # Store shape m.n_vars = A_vec.shape[1] m.n_x = Q.shape[0] @@ -647,7 +647,7 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): m.Q = Q m.A_vec = A_vec # Define the eigenvector matrix - m.V = grad_info["eig_vecs"][:, :r_c] + m.V = grad_info["eig_vecs"][:, : m.r_c] # Define trust region m.trust_reg = opts["trust_reg_init"] m.trust_reg_ub = opts["trust_reg_ub"] @@ -683,13 +683,15 @@ def update_subspace(m, grad_info): certificate matrix """ if m.opts["r_p"] == 0: - m.V = grad_info["eig_vecs"][:, : m.opts["r_c"]] + # TODO: Fix how this works later + m.V = grad_info["min_vec"][:, : m.opts["r_c_max"]] + m.r_c = m.V.shape[1] else: raise NotImplementedError def update_vars(m, opt_info, x_prev, grad_info): """update aggregate matrix variables""" - if m.opts["r_c"] == 1 and m.opts["r_p"] == 0: + if m.r_c == 1 and m.opts["r_p"] == 0: # Get optimization information u = opt_info["u"] eta = opt_info["eta"] @@ -702,7 +704,7 @@ def update_vars(m, opt_info, x_prev, grad_info): eta * m.Q_X + u * grad_info["min_vec"].T @ m.Q @ grad_info["min_vec"] ) - elif m.opts["r_c"] > 1 and m.opts["r_p"] == 0: + elif m.r_c > 1 and m.opts["r_p"] == 0: # Get optimization information U = opt_info["U"] eta = opt_info["eta"] @@ -731,7 +733,7 @@ def update_vars(m, opt_info, x_prev, grad_info): def get_ub(m, grad_info): """Compute upper bound of current model""" - if m.opts["r_c"] == 1 and m.opts["r_p"] == 0: + if m.r_c == 1 and m.opts["r_p"] == 0: # For simplified problem, UB problem is an LP # Inequalities # Set bounds on t level only @@ -794,6 +796,7 @@ def solve_sbm_qp(m, x_curr, grad_info): ) return opt_info + @profile def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): """Solve the spectral bundle method SDP subproblem to find optimal multiplier update. This function should only be called if r_p + r_c = r_bar > 1 @@ -809,7 +812,7 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): _type_: _description_ """ # Define Variables - r_bar = m.opts["r_p"] + m.opts["r_c"] + r_bar = m.opts["r_p"] + m.r_c U = cp.Variable((r_bar, r_bar), symmetric=True) eta = cp.Variable() # Constraints @@ -868,6 +871,7 @@ def update_trust(m, rho, delta_norm): m.penalty = max(A_X_norm / m.trust_reg, 1.0e-8) +@profile def solve_eopt_sbm( Q, A_vec, @@ -891,7 +895,7 @@ def solve_eopt_sbm( kwargs_eig (dict, optional): _description_. Defaults to {}. """ # Update required number of eigenvalues - n_eigs = np.min([opts["r_c"], Q.shape[0]]) + n_eigs = np.min([opts["r_c_max"], Q.shape[0]]) kwargs_eig.update(k=n_eigs) # Intialize status vars for optimization status = "RUNNING" @@ -903,10 +907,11 @@ def solve_eopt_sbm( m = None min_eig_best = -np.inf H = None + tol_mult = 1e-10 while status == "RUNNING": # SOLVE SPECTRAL BUNDLE PROGRAM if n_iter > 0: - if opts["r_c"] == 1 and opts["r_p"] == 0: + if n_iter == 0 or m.r_c == 1: opt_info = m.solve_sbm_qp(x_curr=x_curr, grad_info=grad_info) else: opt_info = m.solve_sbm_sdp(x_curr=x_curr, H_curr=H, grad_info=grad_info) @@ -930,12 +935,13 @@ def solve_eopt_sbm( # Construct Current Certificate matrix H = get_cert_mat(Q, A_vec, x_curr) # Update gradient and eigenvalue - grad_info = get_grad_info(H=H, A_vec=A_vec, **kwargs_eig) + grad_info = get_grad_info(H=H, A_vec=A_vec, tol_mult=tol_mult, **kwargs_eig) # Update model with gradient information if m is None: m = SpectralBundleModel(Q, A_vec, grad_info, opts=opts) else: m.update_subspace(grad_info) + tol_mult = m.r_c # CHECKS if opts["debug"]: assert eig_model >= grad_info["min_eig"] - opts["tol_eig"], Exception( From 257a4838a2a78fc944b4bf36c53a7129bbd083ba Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Thu, 9 Nov 2023 17:15:29 -0500 Subject: [PATCH 15/19] fixed gap convergence issue, led to new issue with computed gradient: model giving negative cost delta prediction. --- cert_tools/eopt_solvers.py | 36 +++++++++++++++++++++--------------- 1 file changed, 21 insertions(+), 15 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 051fa74..02fbd5a 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -55,13 +55,13 @@ tol_null=1e-5, # null space tolerance for first order KKT constraints use_null=True, # if true, reparameterize problem using null space trust_reg_adapt=True, # Use trust region adaptation - trust_reg_init=1e2, # Initial trust region size + trust_reg_init=1e-1, # Initial trust region size trust_reg_ub=1e3, # Trust Region upper bound trust_reg_lb=1e-7, # Trust Region lower bound agreement_req=0.0, # Requirement on model agreement to take a serious step r_c_max=15, # Number of current eigenvectors to keep r_p=0, # Number of previous eigenvectors to keep - tol_mult_eig=1e-3, # Tolerance for multiplicity when adapting r_c + tol_mult_eig=1e-5, # Tolerance for multiplicity when adapting r_c debug=False, # Debugging flag ) @@ -646,6 +646,8 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): # Store constraints and cost m.Q = Q m.A_vec = A_vec + m.A = [A_vec[:, i].reshape(m.n_x, m.n_x, order="F") for i in range(m.n_vars)] + # Define the eigenvector matrix m.V = grad_info["eig_vecs"][:, : m.r_c] # Define trust region @@ -796,7 +798,6 @@ def solve_sbm_qp(m, x_curr, grad_info): ) return opt_info - @profile def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): """Solve the spectral bundle method SDP subproblem to find optimal multiplier update. This function should only be called if r_p + r_c = r_bar > 1 @@ -822,12 +823,20 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): # Objective obj = eta * (m.Q_X + m.A_X.T @ x_curr) obj += cp.trace((m.V.T @ H_curr @ m.V) @ U) - - A_VUV = (m.A_vec.T @ np.kron(m.V, m.V)) @ ( - cp.reshape(U, (r_bar**2, 1), order="F") - ) + VAV = [] + # for i in range(m.n_vars): + # VAV += [(m.V.T @ m.A[i] @ m.V).reshape((1, -1), order="F")] + # VAV_U = np.vstack(VAV) @ cp.vec(U) + # # A_VUV = [cp.trace((m.V.T @ m.A[i] @ m.V) @ U) for i in range(m.n_vars)] + # # A_VUV = cp.vstack(A_VUV) + # A_X = eta * m.A_X[:, 0] + VAV_U + + A_VkV = m.A_vec.T @ np.kron(m.V, m.V) + A_VUV = A_VkV @ cp.vec(U) A_X = eta * m.A_X + A_VUV + obj += 1 / 2 / m.penalty * cp.sum_squares(A_X) + # Define the SDP prob = cp.Problem(cp.Minimize(obj), constraints) sdp_opts = dict(verbose=m.opts["debug"]) @@ -871,7 +880,6 @@ def update_trust(m, rho, delta_norm): m.penalty = max(A_X_norm / m.trust_reg, 1.0e-8) -@profile def solve_eopt_sbm( Q, A_vec, @@ -951,10 +959,9 @@ def solve_eopt_sbm( # STATUS AND VAR UPDATE # Compute the model-objective agreement delta_predict = eig_model - min_eig_best + assert delta_predict > 0, ValueError("predicted cost change is negative") delta_actual = grad_info["min_eig"] - min_eig_best rho_agree = delta_actual / delta_predict - # Relative gap between model and actual - gap_rel = np.abs(delta_actual / min_eig_best) # Update the trust region if m.opts["trust_reg_adapt"]: m.update_trust(rho_agree, delta_norm) @@ -967,9 +974,8 @@ def solve_eopt_sbm( # termination criteria if grad_info["min_eig"] >= -opts["tol_eig"]: # positive lower bound status = "POS_LB" - elif ( - gap_rel * m.penalty < opts["tol_gap"] - ): # converged eigenvalue and not positive + elif delta_predict <= opts["tol_gap"] * (1 + np.abs(min_eig_best)): + # Model converged but mineig not positive status = "GAP" elif m.n_vars == 0: # no variables (i.e. no redundant constraints) status = "NO_VAR" @@ -984,7 +990,7 @@ def solve_eopt_sbm( x=x_curr, min_eig_curr=grad_info["min_eig"], eig_model=eig_model, - gap_rel=gap_rel, + delta_actual=delta_actual, mult=grad_info["t"], rho_agree=rho_agree, ) @@ -1002,7 +1008,7 @@ def solve_eopt_sbm( f" {n_iter:3d} | {delta_norm:5.4e} | {grad_info['min_eig']:5.4e} | {min_eig_best:5.4e} | {eig_model:5.4e} |", end="", ) - print(f" {gap_rel:5.4e} | {m.trust_reg:5.4e} | {grad_info['t']:4d}") + print(f" {delta_actual:5.4e} | {m.trust_reg:5.4e} | {grad_info['t']:4d}") # Update Iterations n_iter += 1 return x_curr, dict( From 72e786e4275912f3b2eefdb21e151668542eeacd Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Fri, 10 Nov 2023 18:11:10 -0500 Subject: [PATCH 16/19] fixes for unit tests. Trying to speed up SDP compute. --- cert_tools/eopt_solvers.py | 48 ++++++++++++++++++++++++-------------- 1 file changed, 31 insertions(+), 17 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index 02fbd5a..bd27a1d 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -50,7 +50,7 @@ # Options for Spectral Bundle Method opts_sbm_dflt = dict( tol_eig=1e-6, # Eigenvalue tolerance - tol_gap=5e-4, # term tolerance on relative gap btwn model eig and best eig + tol_gap=1e-5, # term tolerance on relative gap btwn model eig and best eig max_iter=1000, # Maximum iterations tol_null=1e-5, # null space tolerance for first order KKT constraints use_null=True, # if true, reparameterize problem using null space @@ -798,6 +798,7 @@ def solve_sbm_qp(m, x_curr, grad_info): ) return opt_info + # @profile def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): """Solve the spectral bundle method SDP subproblem to find optimal multiplier update. This function should only be called if r_p + r_c = r_bar > 1 @@ -824,19 +825,19 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): obj = eta * (m.Q_X + m.A_X.T @ x_curr) obj += cp.trace((m.V.T @ H_curr @ m.V) @ U) VAV = [] - # for i in range(m.n_vars): - # VAV += [(m.V.T @ m.A[i] @ m.V).reshape((1, -1), order="F")] - # VAV_U = np.vstack(VAV) @ cp.vec(U) - # # A_VUV = [cp.trace((m.V.T @ m.A[i] @ m.V) @ U) for i in range(m.n_vars)] - # # A_VUV = cp.vstack(A_VUV) - # A_X = eta * m.A_X[:, 0] + VAV_U A_VkV = m.A_vec.T @ np.kron(m.V, m.V) A_VUV = A_VkV @ cp.vec(U) - A_X = eta * m.A_X + A_VUV - + A_X = eta * m.A_X[:, 0] + A_VUV obj += 1 / 2 / m.penalty * cp.sum_squares(A_X) + # cp_vars = cp.hstack([eta, cp.vec(U)]) + # M1 = np.hstack([m.A_X.T @ m.A_X, (m.A_X.T @ A_VkV)]) + # M2 = np.hstack([(m.A_X.T @ A_VkV).T, (A_VkV.T @ A_VkV)]) + # M = np.vstack([M1, M2]) + # M = M + np.eye(M.shape[0]) * 1e-12 + # obj += 1 / 2 / m.penalty * cp.quad_form(cp_vars, M) + # Define the SDP prob = cp.Problem(cp.Minimize(obj), constraints) sdp_opts = dict(verbose=m.opts["debug"]) @@ -848,7 +849,9 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): prob.solve(solver="CVXOPT", **sdp_opts) # Return opt data - opt_info = dict(U=U.value, eta=eta.value, obj_val=obj.value, A_X=A_X.value) + opt_info = dict( + U=U.value, eta=eta.value, obj_val=obj.value, A_X=A_X.value[:, None] + ) return opt_info def update_trust(m, rho, delta_norm): @@ -915,7 +918,6 @@ def solve_eopt_sbm( m = None min_eig_best = -np.inf H = None - tol_mult = 1e-10 while status == "RUNNING": # SOLVE SPECTRAL BUNDLE PROGRAM if n_iter > 0: @@ -932,7 +934,7 @@ def solve_eopt_sbm( delta_x = x_curr - x_prev delta_norm = la.norm(delta_x) # Current model value - eig_model = opt_info["obj_val"][0, 0] + delta_norm**2 * m.penalty / 2 + eig_model = (m.Q_X + m.A_X.T @ x_curr)[0, 0] else: # Init step delta_norm = 0.0 @@ -943,13 +945,14 @@ def solve_eopt_sbm( # Construct Current Certificate matrix H = get_cert_mat(Q, A_vec, x_curr) # Update gradient and eigenvalue - grad_info = get_grad_info(H=H, A_vec=A_vec, tol_mult=tol_mult, **kwargs_eig) + grad_info = get_grad_info( + H=H, A_vec=A_vec, tol_mult=opts["tol_mult_eig"], **kwargs_eig + ) # Update model with gradient information if m is None: m = SpectralBundleModel(Q, A_vec, grad_info, opts=opts) else: m.update_subspace(grad_info) - tol_mult = m.r_c # CHECKS if opts["debug"]: assert eig_model >= grad_info["min_eig"] - opts["tol_eig"], Exception( @@ -959,7 +962,7 @@ def solve_eopt_sbm( # STATUS AND VAR UPDATE # Compute the model-objective agreement delta_predict = eig_model - min_eig_best - assert delta_predict > 0, ValueError("predicted cost change is negative") + assert delta_predict > 0, ValueError("Predicted cost change is negative") delta_actual = grad_info["min_eig"] - min_eig_best rho_agree = delta_actual / delta_predict # Update the trust region @@ -968,9 +971,12 @@ def solve_eopt_sbm( # Check if model-objective agreement is acceptable if rho_agree >= opts["agreement_req"] or n_iter == 0: min_eig_best = grad_info["min_eig"] - else: # If model agreement is bad then don't step + else: + # If model agreement is then reset current step x_curr = x_prev delta_norm = 0.0 + # Recompute certificate matrix + H = get_cert_mat(Q, A_vec, x_curr) # termination criteria if grad_info["min_eig"] >= -opts["tol_eig"]: # positive lower bound status = "POS_LB" @@ -1011,6 +1017,14 @@ def solve_eopt_sbm( print(f" {delta_actual:5.4e} | {m.trust_reg:5.4e} | {grad_info['t']:4d}") # Update Iterations n_iter += 1 + + # Recompute certificate + H = get_cert_mat(Q, A_vec, x_curr) + # Recompute gradient + grad_info = get_grad_info( + H=H, A_vec=A_vec, tol_mult=opts["tol_mult_eig"], **kwargs_eig + ) + return x_curr, dict( min_eig=grad_info["min_eig"], H=H, @@ -1052,7 +1066,7 @@ def plot_along_grad(C, A_vec, mults, step, alpha_max): # Apply step H_alpha = get_cert_mat(C, A_vec, step_alpha) # Check new minimum eigenvalue - grad_info = get_grad_info(H_alpha, A_vec, k=1) + grad_info = get_grad_info(H_alpha, A_vec, k=1, method="direct") min_eigs[i] = grad_info["min_eig"] # Plot min eig From ba9f4cf28c794283d170969394e87d8a12637df6 Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Tue, 14 Nov 2023 14:26:35 -0500 Subject: [PATCH 17/19] Set up trust region properly (no longer uses penalty). --- cert_tools/eopt_solvers.py | 25 +++++++------------------ 1 file changed, 7 insertions(+), 18 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index bd27a1d..ae20333 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -664,11 +664,6 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): if opts["debug"]: # Store actual X (keep unit trace) m.X = m.V @ m.V.T / r_bar - # Initialize the trust region penalty parameter - m.penalty = np.linalg.norm(m.A_X) / m.trust_reg - else: - # Random values (Don't matter) - m.penalty = 1.0 def eval_A_X(m, V): """computes trace(A_i @ V) for each constraint""" @@ -729,8 +724,11 @@ def update_vars(m, opt_info, x_prev, grad_info): else: raise NotImplementedError # Update multipliers - # x = x_prev + m.A_X / np.linalg.norm(m.A_X) * m.trust_reg - x = x_prev + m.A_X / m.penalty + norm_A_X = np.linalg.norm(m.A_X) + if norm_A_X > 0: + x = x_prev + m.trust_reg * m.A_X / norm_A_X + else: + x = x_prev return x def get_ub(m, grad_info): @@ -781,7 +779,7 @@ def solve_sbm_qp(m, x_curr, grad_info): obj = ( eta * (m.Q_X + m.A_X.T @ x_curr) + u * grad_info["min_eig"] - + cp.sum_squares(eta * m.A_X + u * grad_info["subgrad"]) / 2 / m.penalty + + m.trust_reg * cp.norm(eta * m.A_X + u * grad_info["subgrad"], 2) ) # Solve Quadratic Program: prob = cp.Problem(cp.Minimize(obj), constraints) @@ -829,7 +827,7 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): A_VkV = m.A_vec.T @ np.kron(m.V, m.V) A_VUV = A_VkV @ cp.vec(U) A_X = eta * m.A_X[:, 0] + A_VUV - obj += 1 / 2 / m.penalty * cp.sum_squares(A_X) + obj += m.trust_reg * cp.norm(A_X, 2) # cp_vars = cp.hstack([eta, cp.vec(U)]) # M1 = np.hstack([m.A_X.T @ m.A_X, (m.A_X.T @ A_VkV)]) @@ -863,24 +861,15 @@ def update_trust(m, rho, delta_norm): m (_type_): _description_ rho (_type_): _description_ """ - if m.n_vars > 0: - A_X_norm = np.linalg.norm(m.A_X) - else: - A_X_norm = 1.0 # Perform trust region update (See Nocedal and Wright) if rho < 1 / 4: # Shrink trust region m.trust_reg = max(m.trust_reg / 4, m.trust_reg_lb) else: # Expand trust region - trust_reg_actual = A_X_norm / m.penalty - trust_violation = delta_norm - trust_reg_actual - assert trust_violation < 1e-2, ValueError("Trust Region Violated") if rho > 3 / 4: m.trust_reg = min(2 * m.trust_reg, m.trust_reg_ub) # Otherwise keep same region - # Update the penalty - m.penalty = max(A_X_norm / m.trust_reg, 1.0e-8) def solve_eopt_sbm( From 515bce321206208d6d6e9bd98090fdf791c35012 Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Sat, 18 Nov 2023 16:41:58 -0500 Subject: [PATCH 18/19] minor changes to sub and cut schemes to facilitate comparisons over iterations. Changed the sbm method to have an equality on the trace constraints (as per Helmberg paper), introduced intermediate x_step to keep track of null steps and improve readibility. --- cert_tools/eopt_solvers.py | 58 +++++++++++++++++++++++++++----------- 1 file changed, 41 insertions(+), 17 deletions(-) diff --git a/cert_tools/eopt_solvers.py b/cert_tools/eopt_solvers.py index ae20333..9ccaf76 100644 --- a/cert_tools/eopt_solvers.py +++ b/cert_tools/eopt_solvers.py @@ -50,18 +50,19 @@ # Options for Spectral Bundle Method opts_sbm_dflt = dict( tol_eig=1e-6, # Eigenvalue tolerance - tol_gap=1e-5, # term tolerance on relative gap btwn model eig and best eig + tol_gap=1e-7, # term tolerance on relative gap btwn model eig and best eig max_iter=1000, # Maximum iterations tol_null=1e-5, # null space tolerance for first order KKT constraints + tol_grad=1e-12, # tolerance to decide when the gradient is zero. use_null=True, # if true, reparameterize problem using null space trust_reg_adapt=True, # Use trust region adaptation - trust_reg_init=1e-1, # Initial trust region size + trust_reg_init=1e-0, # Initial trust region size trust_reg_ub=1e3, # Trust Region upper bound trust_reg_lb=1e-7, # Trust Region lower bound - agreement_req=0.0, # Requirement on model agreement to take a serious step - r_c_max=15, # Number of current eigenvectors to keep + agreement_req=0.2, # Requirement on model agreement to take a serious step + r_c_max=30, # Number of current eigenvectors to keep r_p=0, # Number of previous eigenvectors to keep - tol_mult_eig=1e-5, # Tolerance for multiplicity when adapting r_c + tol_mult_eig=1e-3, # Tolerance for multiplicity when adapting r_c debug=False, # Debugging flag ) @@ -407,6 +408,7 @@ def solve_eopt_sub( A_eq=None, b_eq=None, xinit=None, + x_cand=None, opts=opts_sub_dflt, verbose=1, kwargs_eig={}, @@ -434,7 +436,7 @@ def solve_eopt_sub( x = xinit print("it \t alpha \t t \t l_min") np.random.seed(1) - + iter_info = [] l_new = None while i <= opts["max_iters"]: H = get_cert_mat(Q, A_vec, x) @@ -444,6 +446,13 @@ def solve_eopt_sub( print(f"multiplicity {t}") if i == 0 and verbose > 0: print(f"start \t ------ \t {t} \t {grad_info['min_eig']:1.4e}") + # Iteration Information + info = dict( + n_iter=i, + x=x.copy(), + min_eig_curr=grad_info["min_eig"], + ) + iter_info += [info] grad = grad_info["subgrad"][:, 0] d = grad / np.linalg.norm(grad) @@ -474,6 +483,7 @@ def solve_eopt_sub( msg = "Converged in stepsize" success = True break + x += alpha * d if verbose > 0: @@ -488,7 +498,18 @@ def solve_eopt_sub( if i == opts["max_iters"]: msg = "Reached maximum iterations" success = False - info = {"success": success, "msg": msg, "min_eig": l_new, "H": H} + if success and (opts["tol_eig"] is not None) and (l_new >= -opts["tol_eig"]): + status = "CERT" + else: + status = "FAIL" + info = { + "success": success, + "status": status, + "msg": msg, + "min_eig": l_new, + "H": H, + "iter_info": pd.DataFrame(iter_info), + } return x, info @@ -646,7 +667,7 @@ def __init__(m, Q, A_vec, grad_info, opts=opts_sbm_dflt): # Store constraints and cost m.Q = Q m.A_vec = A_vec - m.A = [A_vec[:, i].reshape(m.n_x, m.n_x, order="F") for i in range(m.n_vars)] + # m.A = [A_vec[:, i].reshape(m.n_x, m.n_x, order="F") for i in range(m.n_vars)] # Define the eigenvector matrix m.V = grad_info["eig_vecs"][:, : m.r_c] @@ -698,7 +719,8 @@ def update_vars(m, opt_info, x_prev, grad_info): # Update agreggate variables m.A_X = eta * m.A_X + u * grad_info["subgrad"] m.Q_X = ( - eta * m.Q_X + u * grad_info["min_vec"].T @ m.Q @ grad_info["min_vec"] + eta * m.Q_X + + u * grad_info["min_vec"][:, 0].T @ m.Q @ grad_info["min_vec"][:, 0] ) elif m.r_c > 1 and m.opts["r_p"] == 0: @@ -725,7 +747,7 @@ def update_vars(m, opt_info, x_prev, grad_info): raise NotImplementedError # Update multipliers norm_A_X = np.linalg.norm(m.A_X) - if norm_A_X > 0: + if norm_A_X > m.opts["tol_grad"]: x = x_prev + m.trust_reg * m.A_X / norm_A_X else: x = x_prev @@ -774,7 +796,7 @@ def solve_sbm_qp(m, x_curr, grad_info): u = cp.Variable() eta = cp.Variable() # CONSTRAINTS - constraints = [u + eta <= 1.0, u >= 0.0, eta >= 0.0] + constraints = [u + eta == 1.0, u >= 0.0, eta >= 0.0] # Objective obj = ( eta * (m.Q_X + m.A_X.T @ x_curr) @@ -818,7 +840,7 @@ def solve_sbm_sdp(m, x_curr, H_curr, grad_info, verbose=False): # Constraints constraints = [U >> 0] constraints += [eta >= 0] - constraints += [eta + cp.trace(U) <= 1] + constraints += [eta + cp.trace(U) == 1] # Objective obj = eta * (m.Q_X + m.A_X.T @ x_curr) obj += cp.trace((m.V.T @ H_curr @ m.V) @ U) @@ -916,23 +938,24 @@ def solve_eopt_sbm( opt_info = m.solve_sbm_sdp(x_curr=x_curr, H_curr=H, grad_info=grad_info) # Update variables x_prev = x_curr.copy() - x_curr = m.update_vars( + x_step = m.update_vars( opt_info=opt_info, x_prev=x_prev, grad_info=grad_info ) # Compute change in multipliers - delta_x = x_curr - x_prev + delta_x = x_step - x_prev delta_norm = la.norm(delta_x) # Current model value - eig_model = (m.Q_X + m.A_X.T @ x_curr)[0, 0] + eig_model = (m.Q_X + m.A_X.T @ x_step)[0, 0] else: # Init step delta_norm = 0.0 eig_model = np.inf x_prev = x_curr + x_step = x_curr # GET CERTIFICATE AND GRADIENT INFO # Construct Current Certificate matrix - H = get_cert_mat(Q, A_vec, x_curr) + H = get_cert_mat(Q, A_vec, x_step) # Update gradient and eigenvalue grad_info = get_grad_info( H=H, A_vec=A_vec, tol_mult=opts["tol_mult_eig"], **kwargs_eig @@ -960,6 +983,7 @@ def solve_eopt_sbm( # Check if model-objective agreement is acceptable if rho_agree >= opts["agreement_req"] or n_iter == 0: min_eig_best = grad_info["min_eig"] + x_curr = x_step else: # If model agreement is then reset current step x_curr = x_prev @@ -982,7 +1006,7 @@ def solve_eopt_sbm( info = dict( n_iter=n_iter, delta_norm=delta_norm, - x=x_curr, + x=x_step, min_eig_curr=grad_info["min_eig"], eig_model=eig_model, delta_actual=delta_actual, From d34f0fd7e2371b3e786d91f02166b797cd6378bc Mon Sep 17 00:00:00 2001 From: Connor Holmes Date: Mon, 20 Nov 2023 16:54:12 -0500 Subject: [PATCH 19/19] Added script that has code that can generate arbitrary convex hull objectives for the e-opt problem --- _scripts/plot_iters.py | 300 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 300 insertions(+) create mode 100644 _scripts/plot_iters.py diff --git a/_scripts/plot_iters.py b/_scripts/plot_iters.py new file mode 100644 index 0000000..5968737 --- /dev/null +++ b/_scripts/plot_iters.py @@ -0,0 +1,300 @@ +import os, sys +import pickle + +import matplotlib.pyplot as plt + +from matplotlib import cm + +import numpy as np +import scipy.sparse as sp +import scipy.spatial as spatial + +root_dir = os.path.abspath(os.path.dirname(__file__) + "/../") +sys.path.append(root_dir) +from cert_tools.eopt_solvers import * + + +def load_data(prob_file="test_prob_1.pkl"): + try: + with open(os.path.join(root_dir, "_examples", prob_file), "rb") as file: + return pickle.load(file) + except FileNotFoundError: + print(f"Skipping {prob_file} cause file not found.") + return None + + +def run_eopt(data, opts=opts_sbm_dflt, global_min=True, method="cuts"): + # Get global solution + if "x_cand" in data: + x_cand = data["x_cand"] + else: + u, s, v = np.linalg.svd(data["X"]) + x_cand = u[:, [0]] * np.sqrt(s[0]) + # Run optimizer + opts.update(dict(use_null=False)) + Q = data["Q"].copy() + x, output = solve_eopt( + Q=Q, Constraints=data["Constraints"], x_cand=x_cand, opts=opts, method=method + ) + + return output + + +def process_data(data, inds=[0, 1], method="sbm"): + """Preprocess the data down to two multipliers""" + # create vectorized constraints + A_vec_list = [] + for i in range(len(data["Constraints"])): + A, b = data["Constraints"][i] + A_vec_list += [A.reshape((-1, 1), order="F")] + A_vec = sp.hstack(A_vec_list) + + # Run eigenvalue optimization + mults, info = solve_eopt_cuts( + Q=data["Q"], + A_vec=A_vec, + opts=opts_cut_dflt, + xinit=np.array([[0.0, 0.0]]).T, + kwargs_eig=dict(method="direct"), + ) + + Q_bar = data["Q"] + if len(mults) > 2: + # Reduce the set of multipliers + mults_red = [] + A_vec_list = [] + for i in range(len(data["Constraints"])): + A, b = data["Constraints"][i] + if i in inds: + A_vec_list += [A.reshape((-1, 1), order="F")] + mults_red += [mults[i]] + else: + Q_bar += mults[i] * A + A_vec = sp.hstack(A_vec_list) + else: + mults_red = mults + + data.update(dict(Q_bar=Q_bar, A_vec=A_vec, mults=mults_red)) + + return data + + +def plot_obj(data, rng=5): + Q_bar = data["Q_bar"] + A_vec = data["A_vec"] + mults = data["mults"] + # PLOT OBJECTIVE + # Construct ranges + n_pts = 50 + l1 = mults[0] + np.linspace(-rng, rng, n_pts) + l2 = mults[1] + np.linspace(-rng, rng, n_pts) + f = np.zeros((len(l1), len(l2))) + for i in range(len(l1)): + for j in range(len(l2)): + # Get Certificate + H = get_cert_mat(Q_bar, A_vec, [l1[i], l2[j]]) + # Get min eig + grad_info = get_grad_info(H, A_vec, method="direct") + f[i, j] = grad_info["min_eig"] + + # Plot Minimum Eigenvalues + L1, L2 = np.meshgrid(l1, l2) + fig, ax = plt.subplots(subplot_kw=dict(projection="3d")) + surf = ax.plot_surface(L1, L2, f.T, label="min eig", alpha=0.75, cmap=cm.YlGn) + ax.view_init(elev=45, azim=-90, roll=0) + ax.set_aspect("equal") + return fig, ax + + +def plot_iters_sbm(data, x_init, fig, ax): + # RUN OPTIMIZATION + # Run Actual optimization with two multipliers + solver = solve_eopt_sbm + opts = opts_sbm_dflt + alphas, info = solver( + Q=data["Q_bar"], + A_vec=data["A_vec"], + A_eq=None, + b_eq=None, + xinit=x_init, + opts=opts, + kwargs_eig=dict(method="direct"), + ) + print("STATUS:\t" + info["status"]) + # PLOT ITERATIONS + x_vals = info["iter_info"]["x"].values + if x_vals[0].shape[0] == 1: + x_vals = np.vstack(x_vals) + else: + x_vals = np.hstack(x_vals).T + m_eig = info["iter_info"]["min_eig_curr"].values[:, None] + # Select colour based on null step + delta = info["iter_info"]["delta_norm"] + ind = delta > 1e-12 + null = delta < 1e-12 + iter_str = [str(i) for i in info["iter_info"]["n_iter"].values] + ax.scatter3D(x_vals[ind, 0], x_vals[ind, 1], m_eig[ind, 0], marker="o", c="r") + ax.scatter3D( + x_vals[null, 0], x_vals[null, 1], m_eig[null, 0], marker="o", c="b", alpha=0.3 + ) + ax.plot3D(x_vals[:, 0], x_vals[:, 1], m_eig[:, 0], c="b", alpha=0.3) + ax.plot3D(x_vals[ind, 0], x_vals[ind, 1], m_eig[ind, 0], c="r") + for i in range(x_vals.shape[0]): + if ind[i]: + ax.text(x_vals[i, 0], x_vals[i, 1], m_eig[i, 0] + 0.1, iter_str[i]) + + return fig, ax + + +def plot_iters(data, x_init, fig, ax, method="sbm"): + # RUN OPTIMIZATION + # Run Actual optimization with two multipliers + if method == "cuts": + solver = solve_eopt_cuts + opts = opts_cut_dflt + elif method == "sub": + solver = solve_eopt_sub + opts = opts_sub_dflt + elif method == "sbm": + solver = solve_eopt_sbm + opts = opts_sbm_dflt + else: + raise ValueError(f"Unknown method {method} in solve_eopt") + alphas, info = solver( + Q=data["Q_bar"], + A_vec=data["A_vec"], + A_eq=None, + b_eq=None, + xinit=x_init, + opts=opts, + kwargs_eig=dict(method="direct"), + ) + print("STATUS:\t" + info["status"]) + # PLOT ITERATIONS + x_vals = info["iter_info"]["x"].values + if len(x_vals[0].shape) == 1 or x_vals[0].shape[0] == 1: + x_vals = np.vstack(x_vals) + else: + x_vals = np.hstack(x_vals).T + m_eig = info["iter_info"]["min_eig_curr"].values[:, None] + ax.scatter3D(x_vals[:, 0], x_vals[:, 1], m_eig[:, 0], marker="o", c="r") + ax.plot3D(x_vals[:, 0], x_vals[:, 1], m_eig[:, 0], c="r") + + return fig, ax + + +def run_test_prob(prob_file="test_prob_8G.pkl"): + # Get data + data = load_data(prob_file=prob_file) + data = tent_obj() + # process + data = process_data(data, inds=[0, 1]) + # plot objective + fig, ax = plot_obj(data=data, rng=5) + + # SPECTRAL BUNDLE + # plot iterations + x_init = np.array([[0.0, -5.0]]).T + fig, ax = plot_iters_sbm(data, x_init, fig, ax) + ax.set_title("Spectral Bundle Method") + + # CUT PLANE + # plot objective + fig, ax = plot_obj(data=data) + # plot iterations + fig, ax = plot_iters(data, x_init, fig, ax, method="cuts") + ax.set_title("Cut Plane") + + # SUBGRAD + # plot objective + fig, ax = plot_obj(data=data) + # plot iterations + fig, ax = plot_iters(data, x_init, fig, ax, method="sub") + ax.set_title("Subgrad") + + plt.show() + + +def gen_hsphere_cloud(r=1, n_pts=10): + """Generate points on the top hemisphere of a circle""" + pi = np.pi + cos = np.cos + sin = np.sin + phi, theta = np.mgrid[0.0 : pi * 3 / 8 : n_pts * 1j, 0.0 : 2.0 * pi : n_pts * 1j] + x = r * sin(phi) * cos(theta) + y = r * sin(phi) * sin(theta) + z = r * cos(phi) - 0.98 * r + + pts = np.hstack([x.reshape((-1, 1)), y.reshape((-1, 1)), z.reshape((-1, 1))]) + + return pts + + +def get_hsphere_obj(r=1): + # Generate hemisphere points + pts = gen_hsphere_cloud(r=r) + # fig, ax = plt.subplots(subplot_kw={"projection": "3d"}) + # ax.scatter3D(pts[:, 0], pts[:, 1], pts[:, 2]) + plt.show() + # Get convex hull of hsphere points + hull = spatial.ConvexHull(pts) + # get normals and offsets + normals, offsets = hull.equations[:, :3], hull.equations[:, 3] + # Remove down facing normals + ind = normals[:, 2] > 0.0 + normals = normals[ind, :] + offsets = offsets[ind] + # Define Matrices + q = -offsets / normals[:, 2] + B = -normals[:, :2] / normals[:, [2]] + # Q = sp.diags(q) + Q = sp.diags([q, 0.3 * np.ones(len(q) - 1)], [0, 1]) + A_1 = sp.diags(B[:, 0]) + A_2 = sp.diags(B[:, 1]) + Constraints = [(A_1, 0.0), (A_2, 0.0)] + x = np.array([[0, 0]]) + X = x.T @ x + data = dict(Q=Q, Constraints=Constraints, X=X) + + return data + + +def run_sphere_prob(): + # Get data + # data = tent_obj_2() + r = 10 + data = get_hsphere_obj(r=r) + # process + data = process_data(data, inds=[0, 1]) + # plot objective + fig, ax = plot_obj(data=data, rng=r) + + # SPECTRAL BUNDLE + # plot iterations + x_init = np.array([[0.0, -5.0]]).T + fig, ax = plot_iters_sbm(data, x_init, fig, ax) + ax.set_title("Spectral Bundle Method") + + # CUT PLANE + # plot objective + fig, ax = plot_obj(data=data, rng=r) + # plot iterations + fig, ax = plot_iters(data, x_init, fig, ax, method="cuts") + ax.set_title("Cut Plane") + + # SUBGRAD + # plot objective + fig, ax = plot_obj(data=data, rng=r) + # plot iterations + fig, ax = plot_iters(data, x_init, fig, ax, method="sub") + ax.set_title("Subgrad") + + plt.show() + + +if __name__ == "__main__": + # run_test_prob() + # run_tent_prob() + run_sphere_prob() + + print("done")

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