def test_multistart_qei_expected_improvement_dfo(self): """Check that multistart optimization (BFGS) can find the optimum point to sample (using 2-EI).""" numpy.random.seed(7860) index = numpy.argmax(numpy.greater_equal(self.num_sampled_list, 20)) domain, gaussian_process = self.gp_test_environments[index] tolerance = 6.0e-5 num_multistarts = 3 # Expand the domain so that we are definitely not doing constrained optimization expanded_domain = TensorProductDomain([ClosedInterval(-4.0, 3.0)] * self.dim) num_to_sample = 2 repeated_domain = RepeatedDomain(num_to_sample, expanded_domain) num_mc_iterations = 100000 # Just any random point that won't be optimal points_to_sample = repeated_domain.generate_random_point_in_domain() ei_eval = ExpectedImprovement(gaussian_process, points_to_sample, num_mc_iterations=num_mc_iterations) # Compute EI and its gradient for the sake of comparison ei_initial = ei_eval.compute_expected_improvement() ei_optimizer = LBFGSBOptimizer(repeated_domain, ei_eval, self.BFGS_parameters) best_point = multistart_expected_improvement_optimization( ei_optimizer, num_multistarts, num_to_sample) # Check that gradients are "small" or on border. MC is very inaccurate near 0, so use finite difference # gradient instead. ei_eval.current_point = best_point ei_final = ei_eval.compute_expected_improvement() finite_diff_grad = numpy.zeros(best_point.shape) h_value = 0.00001 for i in range(best_point.shape[0]): for j in range(best_point.shape[1]): best_point[i, j] += h_value ei_eval.current_point = best_point ei_upper = ei_eval.compute_expected_improvement() best_point[i, j] -= 2 * h_value ei_eval.current_point = best_point ei_lower = ei_eval.compute_expected_improvement() best_point[i, j] += h_value finite_diff_grad[i, j] = (ei_upper - ei_lower) / (2 * h_value) self.assert_vector_within_relative(finite_diff_grad, numpy.zeros(finite_diff_grad.shape), tolerance) # Check that output is in the domain assert repeated_domain.check_point_inside(best_point) is True # Since we didn't really converge to the optimal EI (too costly), do some other sanity checks # EI should have improved assert ei_final >= ei_initial
def test_multistart_monte_carlo_expected_improvement_optimization(self): """Check that multistart optimization (gradient descent) can find the optimum point to sample (using 2-EI).""" numpy.random.seed(7858) # TODO(271): Monte Carlo only works for this seed index = numpy.argmax(numpy.greater_equal(self.num_sampled_list, 20)) domain, gaussian_process = self.gp_test_environments[index] max_num_steps = 75 # this is *too few* steps; we configure it this way so the test will run quickly max_num_restarts = 5 num_steps_averaged = 50 gamma = 0.2 pre_mult = 1.5 max_relative_change = 1.0 tolerance = 3.0e-2 # really large tolerance b/c converging with monte-carlo (esp in Python) is expensive gd_parameters = GradientDescentParameters( max_num_steps, max_num_restarts, num_steps_averaged, gamma, pre_mult, max_relative_change, tolerance, ) num_multistarts = 2 # Expand the domain so that we are definitely not doing constrained optimization expanded_domain = TensorProductDomain([ClosedInterval(-4.0, 2.0)] * self.dim) num_to_sample = 2 repeated_domain = RepeatedDomain(num_to_sample, expanded_domain) num_mc_iterations = 10000 # Just any random point that won't be optimal points_to_sample = repeated_domain.generate_random_point_in_domain() ei_eval = ExpectedImprovement(gaussian_process, points_to_sample, num_mc_iterations=num_mc_iterations) # Compute EI and its gradient for the sake of comparison ei_initial = ei_eval.compute_expected_improvement(force_monte_carlo=True) # TODO(271) Monte Carlo only works for this seed grad_ei_initial = ei_eval.compute_grad_expected_improvement() ei_optimizer = GradientDescentOptimizer(repeated_domain, ei_eval, gd_parameters) best_point = multistart_expected_improvement_optimization(ei_optimizer, num_multistarts, num_to_sample) # Check that gradients are "small" ei_eval.current_point = best_point ei_final = ei_eval.compute_expected_improvement(force_monte_carlo=True) # TODO(271) Monte Carlo only works for this seed grad_ei_final = ei_eval.compute_grad_expected_improvement() self.assert_vector_within_relative(grad_ei_final, numpy.zeros(grad_ei_final.shape), tolerance) # Check that output is in the domain assert repeated_domain.check_point_inside(best_point) is True # Since we didn't really converge to the optimal EI (too costly), do some other sanity checks # EI should have improved assert ei_final >= ei_initial # grad EI should have improved for index in numpy.ndindex(grad_ei_final.shape): assert numpy.fabs(grad_ei_final[index]) <= numpy.fabs(grad_ei_initial[index])
def test_multistart_qei_expected_improvement_dfo(self): """Check that multistart optimization (BFGS) can find the optimum point to sample (using 2-EI).""" numpy.random.seed(7860) index = numpy.argmax(numpy.greater_equal(self.num_sampled_list, 20)) domain, gaussian_process = self.gp_test_environments[index] tolerance = 6.0e-5 num_multistarts = 3 # Expand the domain so that we are definitely not doing constrained optimization expanded_domain = TensorProductDomain([ClosedInterval(-4.0, 3.0)] * self.dim) num_to_sample = 2 repeated_domain = RepeatedDomain(num_to_sample, expanded_domain) num_mc_iterations = 100000 # Just any random point that won't be optimal points_to_sample = repeated_domain.generate_random_point_in_domain() ei_eval = ExpectedImprovement(gaussian_process, points_to_sample, num_mc_iterations=num_mc_iterations) # Compute EI and its gradient for the sake of comparison ei_initial = ei_eval.compute_expected_improvement() ei_optimizer = LBFGSBOptimizer(repeated_domain, ei_eval, self.BFGS_parameters) best_point = multistart_expected_improvement_optimization(ei_optimizer, num_multistarts, num_to_sample) # Check that gradients are "small" or on border. MC is very inaccurate near 0, so use finite difference # gradient instead. ei_eval.current_point = best_point ei_final = ei_eval.compute_expected_improvement() finite_diff_grad = numpy.zeros(best_point.shape) h_value = 0.00001 for i in range(best_point.shape[0]): for j in range(best_point.shape[1]): best_point[i, j] += h_value ei_eval.current_point = best_point ei_upper = ei_eval.compute_expected_improvement() best_point[i, j] -= 2 * h_value ei_eval.current_point = best_point ei_lower = ei_eval.compute_expected_improvement() best_point[i, j] += h_value finite_diff_grad[i, j] = (ei_upper - ei_lower) / (2 * h_value) self.assert_vector_within_relative(finite_diff_grad, numpy.zeros(finite_diff_grad.shape), tolerance) # Check that output is in the domain assert repeated_domain.check_point_inside(best_point) is True # Since we didn't really converge to the optimal EI (too costly), do some other sanity checks # EI should have improved assert ei_final >= ei_initial