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_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 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 compute_next_points_to_sample_response(self, params, optimizer_method_name, route_name, *args, **kwargs):
"""Compute the next points to sample (and their expected improvement) using optimizer_method_name from params in the request.
.. Warning:: Attempting to find ``num_to_sample`` optimal points with
``num_sampled < num_to_sample`` historical points sampled can cause matrix issues under
some conditions. Try requesting ``num_to_sample < num_sampled`` points for better
performance. To bootstrap more points try sampling at random, or from a grid.
:param request_params: the deserialized REST request, containing ei_optimizer_parameters and gp_historical_info
:type request_params: a deserialized self.request_schema object as a dict
:param optimizer_method_name: the optimization method to use
:type optimizer_method_name: string in :const:`moe.views.constant.NEXT_POINTS_OPTIMIZER_METHOD_NAMES`
:param route_name: name of the route being called
:type route_name: string in :const:`moe.views.constant.ALL_REST_ROUTES_ROUTE_NAME_TO_ENDPOINT`
:param ``*args``: extra args to be passed to optimization method
:param ``**kwargs``: extra kwargs to be passed to optimization method
"""
points_being_sampled = numpy.array(params.get('points_being_sampled'))
num_to_sample = params.get('num_to_sample')
num_mc_iterations = params.get('mc_iterations')
max_num_threads = params.get('max_num_threads')
gaussian_process = _make_gp_from_params(params)
ei_opt_status = {}
# TODO(GH-89): Make the optimal_learning library handle this case 'organically' with
# reasonable default behavior and remove hacks like this one.
if gaussian_process.num_sampled == 0:
# If there is no initial data we bootstrap with random points
py_domain = _make_domain_from_params(params, python_version=True)
next_points = py_domain.generate_uniform_random_points_in_domain(num_to_sample)
ei_opt_status['found_update'] = True
expected_improvement_evaluator = PythonExpectedImprovement(
gaussian_process,
points_being_sampled=points_being_sampled,
num_mc_iterations=num_mc_iterations,
)
else:
# Calculate the next best points to sample given the historical data
optimizer_class, optimizer_parameters, num_random_samples = _make_optimizer_parameters_from_params(params)
if optimizer_class == python_optimization.LBFGSBOptimizer:
domain = RepeatedDomain(num_to_sample, _make_domain_from_params(params, python_version=True))
expected_improvement_evaluator = PythonExpectedImprovement(
gaussian_process,
points_being_sampled=points_being_sampled,
num_mc_iterations=num_mc_iterations,
mvndst_parameters=_make_mvndst_parameters_from_params(params)
)
opt_method = getattr(moe.optimal_learning.python.python_version.expected_improvement, optimizer_method_name)
else:
domain = _make_domain_from_params(params, python_version=False)
expected_improvement_evaluator = ExpectedImprovement(
gaussian_process,
points_being_sampled=points_being_sampled,
num_mc_iterations=num_mc_iterations,
)
opt_method = getattr(moe.optimal_learning.python.cpp_wrappers.expected_improvement, optimizer_method_name)
expected_improvement_optimizer = optimizer_class(
domain,
expected_improvement_evaluator,
optimizer_parameters,
num_random_samples=num_random_samples,
)
with timing_context(EPI_OPTIMIZATION_TIMING_LABEL):
next_points = opt_method(
expected_improvement_optimizer,
params.get('optimizer_info')['num_multistarts'], # optimizer_parameters.num_multistarts,
num_to_sample,
max_num_threads=max_num_threads,
status=ei_opt_status,
*args,
**kwargs
)
# TODO(GH-285): Use analytic q-EI here
# TODO(GH-314): Need to resolve poential issue with NaNs before using q-EI here
# It may be sufficient to check found_update == False in ei_opt_status
# and then use q-EI, else set EI = 0.
expected_improvement_evaluator.current_point = next_points
# The C++ may fail to compute EI with some ``next_points`` inputs (e.g.,
# ``points_to_sample`` and ``points_begin_sampled`` are too close
# together or too close to ``points_sampled``). We catch the exception when this happens
# and attempt a more numerically robust option.
try:
expected_improvement = expected_improvement_evaluator.compute_expected_improvement()
except Exception as exception:
self.log.info('EI computation failed, probably b/c GP-variance matrix is singular. Error: {0:s}'.format(exception))
# ``_compute_expected_improvement_monte_carlo`` in
# :class:`moe.optimal_learning.python.python_version.expected_improvement.ExpectedImprovement`
# has a more reliable (but very expensive) way to deal with singular variance matrices.
python_ei_eval = PythonExpectedImprovement(
expected_improvement_evaluator._gaussian_process,
points_to_sample=next_points,
points_being_sampled=points_being_sampled,
num_mc_iterations=num_mc_iterations,
)
expected_improvement = python_ei_eval.compute_expected_improvement(force_monte_carlo=True)
return self.form_response({
'endpoint': route_name,
'points_to_sample': next_points.tolist(),
'status': {
'expected_improvement': expected_improvement,
'optimizer_success': ei_opt_status,
},
})
def compute_next_points_to_sample_response(self, params,
optimizer_method_name,
route_name, *args, **kwargs):
"""Compute the next points to sample (and their expected improvement) using optimizer_method_name from params in the request.
.. Warning:: Attempting to find ``num_to_sample`` optimal points with
``num_sampled < num_to_sample`` historical points sampled can cause matrix issues under
some conditions. Try requesting ``num_to_sample < num_sampled`` points for better
performance. To bootstrap more points try sampling at random, or from a grid.
:param request_params: the deserialized REST request, containing ei_optimizer_parameters and gp_historical_info
:type request_params: a deserialized self.request_schema object as a dict
:param optimizer_method_name: the optimization method to use
:type optimizer_method_name: string in :const:`moe.views.constant.NEXT_POINTS_OPTIMIZER_METHOD_NAMES`
:param route_name: name of the route being called
:type route_name: string in :const:`moe.views.constant.ALL_REST_ROUTES_ROUTE_NAME_TO_ENDPOINT`
:param ``*args``: extra args to be passed to optimization method
:param ``**kwargs``: extra kwargs to be passed to optimization method
"""
points_being_sampled = numpy.array(params.get('points_being_sampled'))
num_to_sample = params.get('num_to_sample')
num_mc_iterations = params.get('mc_iterations')
max_num_threads = params.get('max_num_threads')
gaussian_process = _make_gp_from_params(params)
ei_opt_status = {}
# TODO(GH-89): Make the optimal_learning library handle this case 'organically' with
# reasonable default behavior and remove hacks like this one.
if gaussian_process.num_sampled == 0:
# If there is no initial data we bootstrap with random points
py_domain = _make_domain_from_params(params, python_version=True)
next_points = py_domain.generate_uniform_random_points_in_domain(
num_to_sample)
ei_opt_status['found_update'] = True
expected_improvement_evaluator = PythonExpectedImprovement(
gaussian_process,
points_being_sampled=points_being_sampled,
num_mc_iterations=num_mc_iterations,
)
else:
# Calculate the next best points to sample given the historical data
optimizer_class, optimizer_parameters, num_random_samples = _make_optimizer_parameters_from_params(
params)
if optimizer_class == python_optimization.LBFGSBOptimizer:
domain = RepeatedDomain(
num_to_sample,
_make_domain_from_params(params, python_version=True))
expected_improvement_evaluator = PythonExpectedImprovement(
gaussian_process,
points_being_sampled=points_being_sampled,
num_mc_iterations=num_mc_iterations,
mvndst_parameters=_make_mvndst_parameters_from_params(
params))
opt_method = getattr(
moe.optimal_learning.python.python_version.
expected_improvement, optimizer_method_name)
else:
domain = _make_domain_from_params(params, python_version=False)
expected_improvement_evaluator = ExpectedImprovement(
gaussian_process,
points_being_sampled=points_being_sampled,
num_mc_iterations=num_mc_iterations,
)
opt_method = getattr(
moe.optimal_learning.python.cpp_wrappers.
expected_improvement, optimizer_method_name)
expected_improvement_optimizer = optimizer_class(
domain,
expected_improvement_evaluator,
optimizer_parameters,
num_random_samples=num_random_samples,
)
with timing_context(EPI_OPTIMIZATION_TIMING_LABEL):
next_points = opt_method(
expected_improvement_optimizer,
params.get('optimizer_info')
['num_multistarts'], # optimizer_parameters.num_multistarts,
num_to_sample,
max_num_threads=max_num_threads,
status=ei_opt_status,
*args,
**kwargs)
# TODO(GH-285): Use analytic q-EI here
# TODO(GH-314): Need to resolve poential issue with NaNs before using q-EI here
# It may be sufficient to check found_update == False in ei_opt_status
# and then use q-EI, else set EI = 0.
expected_improvement_evaluator.current_point = next_points
# The C++ may fail to compute EI with some ``next_points`` inputs (e.g.,
# ``points_to_sample`` and ``points_begin_sampled`` are too close
# together or too close to ``points_sampled``). We catch the exception when this happens
# and attempt a more numerically robust option.
try:
expected_improvement = expected_improvement_evaluator.compute_expected_improvement(
)
except Exception as exception:
self.log.info(
'EI computation failed, probably b/c GP-variance matrix is singular. Error: {0:s}'
.format(exception))
# ``_compute_expected_improvement_monte_carlo`` in
# :class:`moe.optimal_learning.python.python_version.expected_improvement.ExpectedImprovement`
# has a more reliable (but very expensive) way to deal with singular variance matrices.
python_ei_eval = PythonExpectedImprovement(
expected_improvement_evaluator._gaussian_process,
points_to_sample=next_points,
points_being_sampled=points_being_sampled,
num_mc_iterations=num_mc_iterations,
)
expected_improvement = python_ei_eval.compute_expected_improvement(
force_monte_carlo=True)
return self.form_response({
'endpoint': route_name,
'points_to_sample': next_points.tolist(),
'status': {
'expected_improvement': expected_improvement,
'optimizer_success': ei_opt_status,
},
})
