def test_1d_analytic_ei_edge_cases(self):
"""Test cases where analytic EI would attempt to compute 0/0 without variance lower bounds."""
base_coord = numpy.array([0.5])
point1 = SamplePoint(base_coord, -1.809342, 0)
point2 = SamplePoint(base_coord * 2.0, -1.09342, 0)
# First a symmetric case: only one historical point
data = HistoricalData(base_coord.size, [point1])
hyperparameters = numpy.array([0.2, 0.3])
covariance = SquareExponential(hyperparameters)
gaussian_process = GaussianProcess(covariance, data)
point_to_sample = base_coord
ei_eval = ExpectedImprovement(gaussian_process, point_to_sample)
ei = ei_eval.compute_expected_improvement()
grad_ei = ei_eval.compute_grad_expected_improvement()
self.assert_scalar_within_relative(ei, 0.0, 1.0e-15)
self.assert_vector_within_relative(grad_ei, numpy.zeros(grad_ei.shape), 1.0e-15)
shifts = (1.0e-15, 4.0e-11, 3.14e-6, 8.89e-1, 2.71)
self._check_ei_symmetry(ei_eval, point_to_sample, shifts)
# Now introduce some asymmetry with a second point
# Right side has a larger objetive value, so the EI minimum
# is shifted *slightly* to the left of best_so_far.
gaussian_process.add_sampled_points([point2])
shift = 3.0e-12
ei_eval = ExpectedImprovement(gaussian_process, point_to_sample - shift)
ei = ei_eval.compute_expected_improvement()
grad_ei = ei_eval.compute_grad_expected_improvement()
self.assert_scalar_within_relative(ei, 0.0, 1.0e-15)
self.assert_vector_within_relative(grad_ei, numpy.zeros(grad_ei.shape), 1.0e-15)
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_analytic_expected_improvement_optimization(self):
"""Check that multistart optimization (gradient descent) can find the optimum point to sample (using 1D analytic EI)."""
numpy.random.seed(3148)
index = numpy.argmax(numpy.greater_equal(self.num_sampled_list, 20))
domain, gaussian_process = self.gp_test_environments[index]
max_num_steps = 200 # this is generally *too few* steps; we configure it this way so the test will run quickly
max_num_restarts = 5
num_steps_averaged = 0
gamma = 0.2
pre_mult = 1.5
max_relative_change = 1.0
tolerance = 1.0e-7
gd_parameters = GradientDescentParameters(
max_num_steps,
max_num_restarts,
num_steps_averaged,
gamma,
pre_mult,
max_relative_change,
tolerance,
)
num_multistarts = 3
points_to_sample = domain.generate_random_point_in_domain()
ei_eval = ExpectedImprovement(gaussian_process, points_to_sample)
# 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 = 1
repeated_domain = RepeatedDomain(ei_eval.num_to_sample,
expanded_domain)
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
gradient = ei_eval.compute_grad_expected_improvement()
self.assert_vector_within_relative(gradient,
numpy.zeros(gradient.shape),
tolerance)
# Check that output is in the domain
assert repeated_domain.check_point_inside(best_point) is True
def test_multistart_analytic_expected_improvement_optimization(self):
"""Check that multistart optimization (gradient descent) can find the optimum point to sample (using 1D analytic EI)."""
numpy.random.seed(3148)
index = numpy.argmax(numpy.greater_equal(self.num_sampled_list, 20))
domain, gaussian_process = self.gp_test_environments[index]
max_num_steps = 200 # this is generally *too few* steps; we configure it this way so the test will run quickly
max_num_restarts = 5
num_steps_averaged = 0
gamma = 0.2
pre_mult = 1.5
max_relative_change = 1.0
tolerance = 1.0e-7
gd_parameters = GradientDescentParameters(
max_num_steps,
max_num_restarts,
num_steps_averaged,
gamma,
pre_mult,
max_relative_change,
tolerance,
)
num_multistarts = 3
points_to_sample = domain.generate_random_point_in_domain()
ei_eval = ExpectedImprovement(gaussian_process, points_to_sample)
# 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 = 1
repeated_domain = RepeatedDomain(ei_eval.num_to_sample, expanded_domain)
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
gradient = ei_eval.compute_grad_expected_improvement()
self.assert_vector_within_relative(gradient, numpy.zeros(gradient.shape), tolerance)
# Check that output is in the domain
assert repeated_domain.check_point_inside(best_point) is True
