def test_gradient_descent_optimizer_constrained(self):
"""Check that gradient descent can find the global optimum (in a domain) when the true optimum is outside."""
# Domain where the optimum, (0.5, 0.5, 0.5), lies outside the domain
domain_bounds = [ClosedInterval(0.05, 0.32), ClosedInterval(0.05, 0.6), ClosedInterval(0.05, 0.32)]
domain = TensorProductDomain(domain_bounds)
gradient_descent_optimizer = GradientDescentOptimizer(domain, self.polynomial, self.gd_parameters)
# Work out what the maxima point woudl be given the domain constraints (i.e., project to the nearest point on domain)
constrained_optimum_point = self.polynomial.optimum_point
for i, bounds in enumerate(domain_bounds):
if constrained_optimum_point[i] > bounds.max:
constrained_optimum_point[i] = bounds.max
elif constrained_optimum_point[i] < bounds.min:
constrained_optimum_point[i] = bounds.min
tolerance = 2.0e-13
initial_guess = numpy.full(self.polynomial.dim, 0.2)
gradient_descent_optimizer.objective_function.current_point = initial_guess
initial_value = gradient_descent_optimizer.objective_function.compute_objective_function()
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
# Verify coordinates
self.assert_vector_within_relative(output, constrained_optimum_point, tolerance)
# Verify optimized value is better than initial guess
final_value = self.polynomial.compute_objective_function()
T.assert_gt(final_value, initial_value)
# Verify derivative: only get 0 derivative if the coordinate lies inside domain boundaries
gradient = self.polynomial.compute_grad_objective_function()
for i, bounds in enumerate(domain_bounds):
if bounds.is_inside(self.polynomial.optimum_point[i]):
self.assert_scalar_within_relative(gradient[i], 0.0, tolerance)
def test_gradient_descent_optimizer(self):
"""Check that gradient descent can find the optimum of the quadratic test objective."""
# Check the claimed optima is an optima
optimum_point = self.polynomial.optimum_point
self.polynomial.current_point = optimum_point
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient, numpy.zeros(self.polynomial.dim), 0.0)
# Verify that gradient descent does not move from the optima if we start it there.
gradient_descent_optimizer = GradientDescentOptimizer(self.domain, self.polynomial, self.gd_parameters)
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
self.assert_vector_within_relative(output, optimum_point, 0.0)
# Start at a wrong point and check optimization
tolerance = 2.0e-13
initial_guess = numpy.full(self.polynomial.dim, 0.2)
gradient_descent_optimizer.objective_function.current_point = initial_guess
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
# Verify coordinates
self.assert_vector_within_relative(output, optimum_point, tolerance)
# Verify function value
value = self.polynomial.compute_objective_function()
self.assert_scalar_within_relative(value, self.polynomial.optimum_value, tolerance)
# Verify derivative
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient, numpy.zeros(self.polynomial.dim), tolerance)
def test_gradient_descent_optimizer_with_averaging(self):
"""Check that gradient descent can find the optimum of the quadratic test objective with averaging on.
This test doesn't exercise the purpose of averaging (i.e., this objective isn't stochastic), but it does
check that it at least runs.
"""
num_steps_averaged = self.gd_parameters.max_num_steps * 3 / 4
gd_parameters_averaging = GradientDescentParameters(
self.gd_parameters.max_num_steps,
self.gd_parameters.max_num_restarts,
num_steps_averaged,
self.gd_parameters.gamma,
self.gd_parameters.pre_mult,
self.gd_parameters.max_relative_change,
self.gd_parameters.tolerance,
)
# Check the claimed optima is an optima
optimum_point = self.polynomial.optimum_point
self.polynomial.current_point = optimum_point
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient,
numpy.zeros(self.polynomial.dim),
0.0)
# Verify that gradient descent does not move from the optima if we start it there.
gradient_descent_optimizer = GradientDescentOptimizer(
self.domain, self.polynomial, gd_parameters_averaging)
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
self.assert_vector_within_relative(output, optimum_point, 0.0)
# Start at a wrong point and check optimization
tolerance = 2.0e-10
initial_guess = numpy.full(self.polynomial.dim, 0.2)
gradient_descent_optimizer.objective_function.current_point = initial_guess
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
# Verify coordinates
self.assert_vector_within_relative(output, optimum_point, tolerance)
# Verify function value
value = self.polynomial.compute_objective_function()
self.assert_scalar_within_relative(value,
self.polynomial.optimum_value,
tolerance)
# Verify derivative
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient,
numpy.zeros(self.polynomial.dim),
tolerance)
def test_gradient_descent_optimizer_with_averaging(self):
"""Check that gradient descent can find the optimum of the quadratic test objective with averaging on.
This test doesn't exercise the purpose of averaging (i.e., this objective isn't stochastic), but it does
check that it at least runs.
"""
num_steps_averaged = self.gd_parameters.max_num_steps * 3 / 4
gd_parameters_averaging = GradientDescentParameters(
self.gd_parameters.max_num_steps,
self.gd_parameters.max_num_restarts,
num_steps_averaged,
self.gd_parameters.gamma,
self.gd_parameters.pre_mult,
self.gd_parameters.max_relative_change,
self.gd_parameters.tolerance,
)
# Check the claimed optima is an optima
optimum_point = self.polynomial.optimum_point
self.polynomial.current_point = optimum_point
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient, numpy.zeros(self.polynomial.dim), 0.0)
# Verify that gradient descent does not move from the optima if we start it there.
gradient_descent_optimizer = GradientDescentOptimizer(self.domain, self.polynomial, gd_parameters_averaging)
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
self.assert_vector_within_relative(output, optimum_point, 0.0)
# Start at a wrong point and check optimization
tolerance = 2.0e-10
initial_guess = numpy.full(self.polynomial.dim, 0.2)
gradient_descent_optimizer.objective_function.current_point = initial_guess
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
# Verify coordinates
self.assert_vector_within_relative(output, optimum_point, tolerance)
# Verify function value
value = self.polynomial.compute_objective_function()
self.assert_scalar_within_relative(value, self.polynomial.optimum_value, tolerance)
# Verify derivative
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient, numpy.zeros(self.polynomial.dim), tolerance)
def test_gradient_descent_optimizer_constrained(self):
"""Check that gradient descent can find the global optimum (in a domain) when the true optimum is outside."""
# Domain where the optimum, (0.5, 0.5, 0.5), lies outside the domain
domain_bounds = [
ClosedInterval(0.05, 0.32),
ClosedInterval(0.05, 0.6),
ClosedInterval(0.05, 0.32)
]
domain = TensorProductDomain(domain_bounds)
gradient_descent_optimizer = GradientDescentOptimizer(
domain, self.polynomial, self.gd_parameters)
# Work out what the maxima point woudl be given the domain constraints (i.e., project to the nearest point on domain)
constrained_optimum_point = self.polynomial.optimum_point
for i, bounds in enumerate(domain_bounds):
if constrained_optimum_point[i] > bounds.max:
constrained_optimum_point[i] = bounds.max
elif constrained_optimum_point[i] < bounds.min:
constrained_optimum_point[i] = bounds.min
tolerance = 2.0e-13
initial_guess = numpy.full(self.polynomial.dim, 0.2)
gradient_descent_optimizer.objective_function.current_point = initial_guess
initial_value = gradient_descent_optimizer.objective_function.compute_objective_function(
)
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
# Verify coordinates
self.assert_vector_within_relative(output, constrained_optimum_point,
tolerance)
# Verify optimized value is better than initial guess
final_value = self.polynomial.compute_objective_function()
assert final_value >= initial_value
# Verify derivative: only get 0 derivative if the coordinate lies inside domain boundaries
gradient = self.polynomial.compute_grad_objective_function()
for i, bounds in enumerate(domain_bounds):
if bounds.is_inside(self.polynomial.optimum_point[i]):
self.assert_scalar_within_relative(gradient[i], 0.0, tolerance)
def test_gradient_descent_optimizer(self):
"""Check that gradient descent can find the optimum of the quadratic test objective."""
# Check the claimed optima is an optima
optimum_point = self.polynomial.optimum_point
self.polynomial.current_point = optimum_point
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient,
numpy.zeros(self.polynomial.dim),
0.0)
# Verify that gradient descent does not move from the optima if we start it there.
gradient_descent_optimizer = GradientDescentOptimizer(
self.domain, self.polynomial, self.gd_parameters)
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
self.assert_vector_within_relative(output, optimum_point, 0.0)
# Start at a wrong point and check optimization
tolerance = 2.0e-13
initial_guess = numpy.full(self.polynomial.dim, 0.2)
gradient_descent_optimizer.objective_function.current_point = initial_guess
gradient_descent_optimizer.optimize()
output = gradient_descent_optimizer.objective_function.current_point
# Verify coordinates
self.assert_vector_within_relative(output, optimum_point, tolerance)
# Verify function value
value = self.polynomial.compute_objective_function()
self.assert_scalar_within_relative(value,
self.polynomial.optimum_value,
tolerance)
# Verify derivative
gradient = self.polynomial.compute_grad_objective_function()
self.assert_vector_within_relative(gradient,
numpy.zeros(self.polynomial.dim),
tolerance)