def test_nesterovmomentum_optimizer_univar(self, x_start, tol):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for univariate functions."""
stepsize, gamma = 0.1, 0.5
nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
univariate_funcs = [np.sin, lambda x: np.exp(x / 10.0), lambda x: x ** 2]
grad_uni_fns = [
lambda x: (np.cos(x),),
lambda x: (np.exp(x / 10.0) / 10.0,),
lambda x: (2 * x,),
]
for gradf, f in zip(grad_uni_fns, univariate_funcs):
nesmom_opt.reset()
x_onestep = nesmom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start)[0] * stepsize
assert np.allclose(x_onestep, x_onestep_target, atol=tol)
x_twosteps = nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)[0]
shifted_grad_term = gradf(x_onestep - stepsize * momentum_term)[0]
x_twosteps_target = x_onestep - (shifted_grad_term + momentum_term) * stepsize
assert np.allclose(x_twosteps, x_twosteps_target, atol=tol)
def test_nesterovmomentum_optimizer_multivar(self, tol):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for multivariate functions."""
stepsize, gamma = 0.1, 0.5
nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_ ** 2 for x_ in x]),
]
grad_multi_funcs = [
lambda x: (np.array([np.cos(x[0]), -np.sin(x[1])]),),
lambda x: (
np.array(
[
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1]) ** 2),
]
),
),
lambda x: (np.array([2 * x_ for x_ in x]),),
]
x_vals = np.linspace(-10, 10, 16, endpoint=False)
for gradf, f in zip(grad_multi_funcs, multivariate_funcs):
for jdx in range(len(x_vals[:-1])):
nesmom_opt.reset()
x_vec = x_vals[jdx : jdx + 2]
x_onestep = nesmom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec)[0] * stepsize
assert np.allclose(x_onestep, x_onestep_target, atol=tol)
x_twosteps = nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)[0]
shifted_grad_term = gradf(x_onestep - stepsize * momentum_term)[0]
x_twosteps_target = x_onestep - (shifted_grad_term + momentum_term) * stepsize
assert np.allclose(x_twosteps, x_twosteps_target, atol=tol)
class BasicTest(BaseTest):
"""Basic optimizer tests.
"""
def setUp(self):
self.sgd_opt = GradientDescentOptimizer(stepsize)
self.mom_opt = MomentumOptimizer(stepsize, momentum=gamma)
self.nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
self.adag_opt = AdagradOptimizer(stepsize)
self.rms_opt = RMSPropOptimizer(stepsize, decay=gamma)
self.adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
self.fnames = ['test_function_1', 'test_function_2', 'test_function_3']
self.univariate_funcs = [
np.sin, lambda x: np.exp(x / 10.), lambda x: x**2
]
self.grad_uni_fns = [
np.cos, lambda x: np.exp(x / 10.) / 10., lambda x: 2 * x
]
self.multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_**2 for x_ in x])
]
self.grad_multi_funcs = [
lambda x: np.array([np.cos(x[0]), -np.sin(x[1])]),
lambda x: np.array([
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1])**2)
]), lambda x: np.array([2 * x_ for x_ in x])
]
self.mvar_mdim_funcs = [
lambda x: np.sin(x[0, 0]) + np.cos(x[1, 0]) - np.sin(x[0, 1]) + x[
1, 1], lambda x: np.exp(x[0, 0] / 3) * np.tanh(x[0, 1]),
lambda x: np.sum([x_[0]**2 for x_ in x])
]
self.grad_mvar_mdim_funcs = [
lambda x: np.array([[np.cos(x[0, 0]), -np.cos(x[0, 1])],
[-np.sin(x[1, 0]), 1.]]),
lambda x: np.array([[
np.exp(x[0, 0] / 3) / 3 * np.tanh(x[0, 1]),
np.exp(x[0, 0] / 3) * (1 - np.tanh(x[0, 1])**2)
], [0., 0.]]), lambda x: np.array([[2 * x_[0], 0.] for x_ in x])
]
self.class_fun = class_fun
self.quant_fun = quant_fun
self.hybrid_fun = hybrid_fun
self.hybrid_fun_nested = hybrid_fun_nested
self.hybrid_fun_flat = hybrid_fun_flat
self.hybrid_fun_mdarr = hybrid_fun_mdarr
self.hybrid_fun_mdlist = hybrid_fun_mdlist
self.mixed_list = [(0.2, 0.3), np.array([0.4, 0.2, 0.4]), 0.1]
self.mixed_tuple = (np.array([0.2, 0.3]), [0.4, 0.2, 0.4], 0.1)
self.nested_list = [[[0.2], 0.3], [0.1, [0.4]], -0.1]
self.flat_list = [0.2, 0.3, 0.1, 0.4, -0.1]
self.multid_array = np.array([[0.1, 0.2], [-0.1, -0.4]])
self.multid_list = [[0.1, 0.2], [-0.1, -0.4]]
def test_mixed_inputs_for_hybrid_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for hybrid optimization tasks."""
self.logTestName()
hybrid_list = self.sgd_opt.step(self.hybrid_fun, self.mixed_list)
hybrid_tuple = self.sgd_opt.step(self.hybrid_fun, self.mixed_tuple)
self.assertAllAlmostEqual(hybrid_list[0],
hybrid_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(hybrid_list[1],
hybrid_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(hybrid_list[2],
hybrid_tuple[2],
delta=self.tol)
def test_mixed_inputs_for_classical_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for purely classical optimization tasks."""
self.logTestName()
class_list = self.sgd_opt.step(self.class_fun, self.mixed_list)
class_tuple = self.sgd_opt.step(self.class_fun, self.mixed_tuple)
self.assertAllAlmostEqual(class_list[0],
class_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(class_list[1],
class_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(class_list[2],
class_tuple[2],
delta=self.tol)
def test_mixed_inputs_for_quantum_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for purely quantum optimization tasks."""
self.logTestName()
quant_list = self.sgd_opt.step(self.quant_fun, self.mixed_list)
quant_tuple = self.sgd_opt.step(self.quant_fun, self.mixed_tuple)
self.assertAllAlmostEqual(quant_list[0],
quant_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(quant_list[1],
quant_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(quant_list[2],
quant_tuple[2],
delta=self.tol)
def test_nested_and_flat_returns_same_update(self):
"""Tests that gradient descent optimizer has the same output for
nested and flat lists."""
self.logTestName()
nested = self.sgd_opt.step(self.hybrid_fun_nested, self.nested_list)
flat = self.sgd_opt.step(self.hybrid_fun_flat, self.flat_list)
self.assertAllAlmostEqual(flat, list(_flatten(nested)), delta=self.tol)
def test_array_and_list_return_same_update(self):
"""Tests that gradient descent optimizer has the same output for
lists and arrays."""
self.logTestName()
array = self.sgd_opt.step(self.hybrid_fun_mdarr, self.multid_array)
list = self.sgd_opt.step(self.hybrid_fun_mdlist, self.multid_list)
self.assertAllAlmostEqual(array, list, delta=self.tol)
def test_gradient_descent_optimizer_univar(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
x_new = self.sgd_opt.step(f, x_start)
x_correct = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_new, x_correct, delta=self.tol)
def test_gradient_descent_optimizer_multivar(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
x_vec = x_vals[jdx:jdx + 2]
x_new = self.sgd_opt.step(f, x_vec)
x_correct = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_new, x_correct, delta=self.tol)
def test_gradient_descent_optimizer_multivar_multidim(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multi-variate functions and with higher dimensional inputs."""
self.logTestName()
for gradf, f, name in zip(self.grad_mvar_mdim_funcs,
self.mvar_mdim_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-3])):
x_vec = x_vals[jdx:jdx + 4]
x_vec_multidim = np.reshape(x_vec, (2, 2))
x_new = self.sgd_opt.step(f, x_vec_multidim)
x_correct = x_vec_multidim - gradf(
x_vec_multidim) * stepsize
x_new_flat = x_new.flatten()
x_correct_flat = x_correct.flatten()
self.assertAllAlmostEqual(x_new_flat,
x_correct_flat,
delta=self.tol)
def test_gradient_descent_optimizer_usergrad(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
using user-provided gradients."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns[::-1],
self.univariate_funcs, self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
x_new = self.sgd_opt.step(f, x_start, grad_fn=gradf)
x_correct = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_new, x_correct, delta=self.tol)
def test_momentum_optimizer_univar(self):
"""Tests that momentum optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.mom_opt.reset()
x_onestep = self.mom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.mom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)
x_twosteps_target = x_onestep - (gradf(x_onestep) +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_momentum_optimizer_multivar(self):
"""Tests that momentum optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.mom_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.mom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.mom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)
x_twosteps_target = x_onestep - (gradf(x_onestep) +
momentum_term) * stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_univar(self):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.nesmom_opt.reset()
x_onestep = self.nesmom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_multivar(self):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.nesmom_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.nesmom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_usergrad(self):
"""Tests that nesterov momentum optimizer takes gradient-descent steps correctly
using user-provided gradients."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns[::-1],
self.univariate_funcs, self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.nesmom_opt.reset()
x_onestep = self.nesmom_opt.step(f, x_start, grad_fn=gradf)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f,
x_onestep,
grad_fn=gradf)
momentum_term = gamma * gradf(x_start)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adagrad_optimizer_univar(self):
"""Tests that adagrad optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.adag_opt.reset()
x_onestep = self.adag_opt.step(f, x_start)
past_grads = gradf(x_start) * gradf(x_start)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_start - gradf(
x_start) * adapt_stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adag_opt.step(f, x_onestep)
past_grads = gradf(x_start) * gradf(x_start) + gradf(
x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adagrad_optimizer_multivar(self):
"""Tests that adagrad optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.adag_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.adag_opt.step(f, x_vec)
past_grads = gradf(x_vec) * gradf(x_vec)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_vec - gradf(x_vec) * adapt_stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adag_opt.step(f, x_onestep)
past_grads = gradf(x_vec) * gradf(x_vec) + gradf(
x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_rmsprop_optimizer_univar(self):
"""Tests that rmsprop optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.rms_opt.reset()
x_onestep = self.rms_opt.step(f, x_start)
past_grads = (1 - gamma) * gradf(x_start) * gradf(x_start)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_start - gradf(
x_start) * adapt_stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.rms_opt.step(f, x_onestep)
past_grads = (1 - gamma) * gamma * gradf(x_start)*gradf(x_start) \
+ (1 - gamma) * gradf(x_onestep)*gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_rmsprop_optimizer_multivar(self):
"""Tests that rmsprop optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.rms_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.rms_opt.step(f, x_vec)
past_grads = (1 - gamma) * gradf(x_vec) * gradf(x_vec)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_vec - gradf(x_vec) * adapt_stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.rms_opt.step(f, x_onestep)
past_grads = (1 - gamma) * gamma * gradf(x_vec) * gradf(x_vec) \
+ (1 - gamma) * gradf(x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adam_optimizer_univar(self):
"""Tests that adam optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.adam_opt.reset()
x_onestep = self.adam_opt.step(f, x_start)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 -
gamma)
firstmoment = gradf(x_start)
secondmoment = gradf(x_start) * gradf(x_start)
x_onestep_target = x_start - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta**2) / (
1 - gamma**2)
firstmoment = (gamma * gradf(x_start) +
(1 - gamma) * gradf(x_onestep))
secondmoment = (
delta * gradf(x_start) * gradf(x_start) +
(1 - delta) * gradf(x_onestep) * gradf(x_onestep))
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adam_optimizer_multivar(self):
"""Tests that adam optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.adam_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.adam_opt.step(f, x_vec)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 -
gamma)
firstmoment = gradf(x_vec)
secondmoment = gradf(x_vec) * gradf(x_vec)
x_onestep_target = x_vec - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta**2) / (
1 - gamma**2)
firstmoment = (gamma * gradf(x_vec) +
(1 - gamma) * gradf(x_onestep))
secondmoment = (
delta * gradf(x_vec) * gradf(x_vec) +
(1 - delta) * gradf(x_onestep) * gradf(x_onestep))
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)