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_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_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 optimize(self, all_x):
"""
:param all_x:
:return: (best_point, found_point_successfully)
"""
ei_evaluator = ExpectedImprovement(self._gp)
ei_vals = numpy.zeros(len(all_x))
for i in range(len(ei_vals)):
ei_evaluator.set_current_point(all_x[i, :].reshape((1, -1)))
print ei_evaluator.num_to_sample
ei_vals[i] = ei_evaluator.compute_expected_improvement()
best_ei = numpy.amax(ei_vals)
if best_ei > 0:
return all_x[numpy.argmax(best_ei), :], True
else:
return all_x[numpy.random.randint(low=0, high=len(best_ei), size=1
), :], False
def test_evaluate_ei_at_points(self):
"""Check that ``evaluate_expected_improvement_at_point_list`` computes and orders results correctly (using 1D analytic EI)."""
index = numpy.argmax(numpy.greater_equal(self.num_sampled_list, 5))
domain, gaussian_process = self.gp_test_environments[index]
points_to_sample = domain.generate_random_point_in_domain()
ei_eval = ExpectedImprovement(gaussian_process, points_to_sample)
num_to_eval = 10
# Add in a newaxis to make num_to_sample explicitly 1
points_to_evaluate = domain.generate_uniform_random_points_in_domain(num_to_eval)[:, numpy.newaxis, :]
test_values = ei_eval.evaluate_at_point_list(points_to_evaluate)
for i, value in enumerate(test_values):
ei_eval.current_point = points_to_evaluate[i, ...]
truth = ei_eval.compute_expected_improvement()
assert value == truth
def optimize_with_ego(gp, domain_bounds, num_multistart):
expected_improvement_evaluator = ExpectedImprovement(gp)
search_domain = pythonTensorProductDomain(
[ClosedInterval(bound[0], bound[1]) for bound in domain_bounds])
start_points = search_domain.generate_uniform_random_points_in_domain(
num_multistart)
min_negative_ei = numpy.inf
def negative_ego_func(x):
expected_improvement_evaluator.set_current_point(x.reshape((1, -1)))
return -1.0 * expected_improvement_evaluator.compute_expected_improvement(
)
for start_point in start_points:
x, f = bfgs_optimization(start_point, negative_ego_func, domain_bounds)
if min_negative_ei > f:
min_negative_ei = f
point_to_sample = x
return point_to_sample, -min_negative_ei
def test_expected_improvement_and_gradient(self):
"""Test EI by comparing the vectorized and "naive" versions.
With the same RNG state, these two functions should return identical output.
We use a fairly low number of monte-carlo iterations since we are not
trying to converge; just check for consistency.
.. Note:: this is not a particularly good test. It relies on the "naive"
version being easier to verify manually and only checks for consistency
between the naive and vectorized versions.
"""
num_points_p_q_list = ((1, 0), (1, 1), (2, 1), (1, 4), (5, 3))
ei_tolerance = 10.0 * numpy.finfo(numpy.float64).eps
grad_ei_tolerance = 1.0e-13
numpy.random.seed(78532)
for test_case in self.gp_test_environments:
domain, gaussian_process = test_case
for num_to_sample, num_being_sampled in num_points_p_q_list:
points_to_sample = domain.generate_uniform_random_points_in_domain(num_to_sample)
points_being_sampled = domain.generate_uniform_random_points_in_domain(num_being_sampled)
union_of_points = numpy.reshape(numpy.append(points_to_sample, points_being_sampled), (num_to_sample + num_being_sampled, self.dim))
ei_eval = ExpectedImprovement(
gaussian_process,
points_to_sample,
points_being_sampled=points_being_sampled,
num_mc_iterations=self.num_mc_iterations,
)
# Compute quantities required for EI
mu_star = ei_eval._gaussian_process.compute_mean_of_points(union_of_points)
var_star = ei_eval._gaussian_process.compute_variance_of_points(union_of_points)
# Check EI
# Save state first to restore at the end (o/w other "random" events will get screwed up)
rng_state = numpy.random.get_state()
numpy.random.seed(self.rng_seed)
ei_vectorized = ei_eval._compute_expected_improvement_monte_carlo(mu_star, var_star)
numpy.random.seed(self.rng_seed)
ei_naive = ei_eval._compute_expected_improvement_monte_carlo_naive(mu_star, var_star)
self.assert_scalar_within_relative(ei_vectorized, ei_naive, ei_tolerance)
# Compute quantities required for grad EI
grad_mu = ei_eval._gaussian_process.compute_grad_mean_of_points(
union_of_points,
num_derivatives=num_to_sample,
)
grad_chol_decomp = ei_eval._gaussian_process.compute_grad_cholesky_variance_of_points(
union_of_points,
num_derivatives=num_to_sample,
)
# Check grad EI
numpy.random.seed(self.rng_seed)
grad_ei_vectorized = ei_eval._compute_grad_expected_improvement_monte_carlo(
mu_star,
var_star,
grad_mu,
grad_chol_decomp,
)
numpy.random.seed(self.rng_seed)
grad_ei_naive = ei_eval._compute_grad_expected_improvement_monte_carlo_naive(
mu_star,
var_star,
grad_mu,
grad_chol_decomp,
)
self.assert_vector_within_relative(grad_ei_vectorized, grad_ei_naive, grad_ei_tolerance)
# Restore state
numpy.random.set_state(rng_state)
# data containers for pickle storage
list_best = []
list_cost = []
list_sampled_IS = []
list_sampled_points = []
list_sampled_vals = []
list_noise_var = []
list_raw_voi = []
best_sampled_val = np.amin(problem.hist_data._points_sampled_value)
truth_at_init_best_sampled = problem.obj_func_min.evaluate(
problem.truth_is, problem.hist_data.points_sampled[
np.argmin(problem.hist_data._points_sampled_value), :])
truth_at_best_sampled = truth_at_init_best_sampled
total_cost = 0.0
for ego_n in range(problem.num_iterations):
expected_improvement_evaluator = ExpectedImprovement(ego_gp)
min_negative_ei = np.inf
def negative_ego_func(x):
expected_improvement_evaluator.set_current_point(x.reshape((1, -1)))
return -1.0 * expected_improvement_evaluator.compute_expected_improvement(
)
def negative_ego_grad_func(x):
expected_improvement_evaluator.set_current_point(x.reshape((1, -1)))
return -1.0 * expected_improvement_evaluator.compute_grad_expected_improvement(
)[0, :]
def min_negative_ego_func(start_point):
return bfgs_optimization_grad(start_point, negative_ego_func,
negative_ego_grad_func,
