def test_UPGM_on_third_analytical_example_non_zero_start():
print(
'# Test UPGM on Third Analytical Example (constrained dual). Start at NON-0.'
)
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = ConstrainedDualAnalyticalExampleInnerProblem()
dual_method = UniversalPGM(analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension)
# we set the initial point somewhere not 0
dual_method.lambda_hat_k = dual_method.projection_function(
np.array([-2, 2]))
logger = GenericDualMethodLogger(dual_method)
for iteration in range(5):
# print(dual_method.lambda_k)
# print(dual_method.lambda_tilde_k)
# print(dual_method.d_k)
dual_method.dual_step()
# Method should end close to lambda*, where lambda*[1] = 0.5 - lambda*[0], and 0<= lambda*[0] <= 0.5
lambda_star = logger.lambda_k_iterates[-1]
# print(lambda_star)
assert 0 <= lambda_star[0] <= 0.5
assert lambda_star[1] == 0.5 - lambda_star[0]
# with value close to dual optimum
np.testing.assert_allclose(logger.d_k_iterates[-1], -1.0, atol=0.01)
def test_averaged_UPGM_on_analytical_example():
print('# Test averaged UPGM on Analytical Example')
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = AnalyticalExampleInnerProblem()
dual_method = UniversalPGM(analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension,
epsilon=0.01,
averaging=True)
logger = GenericDualMethodLogger(dual_method)
for iteration in range(50):
# print(dual_method.S_k)
# print(dual_method.lambda_k)
# print(dual_method.d_k)
dual_method.dual_step()
# When averaging is turned on, method is much slower. Method should end close to lambda* but get to about [0.3, 0.7]
np.testing.assert_allclose(logger.lambda_k_iterates[-1],
np.array([0.3, 0.7]),
atol=0.1)
# should be close to optimal value (-0.5) but is at -0.8
np.testing.assert_allclose(logger.d_k_iterates[-1], -0.8, atol=0.1)
def test_averaged_UFGM_on_analytical_example():
print('# Test Averaged UFGM on Analytical Example')
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = AnalyticalExampleInnerProblem()
dual_method = UniversalFGM(analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension,
epsilon=0.1,
averaging=False)
logger = GenericDualMethodLogger(dual_method)
for iteration in range(40):
# print(dual_method.lambda_k)
# print dual_method.d_k
dual_method.dual_step()
# Method should end close to lambda*
np.testing.assert_allclose(logger.lambda_k_iterates[-1],
np.array([1., 1.]),
rtol=1e-1,
atol=0)
# with value close to dual optimum
np.testing.assert_allclose(logger.d_k_iterates[-1],
-0.5,
rtol=1e-1,
atol=0)
def test_subgradient_method_on_analytical_example():
print('# Test Subgradient Method on Analytical Example (2 ineq)')
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = AnalyticalExampleInnerProblem()
dual_method = SubgradientMethod(
analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension,
sense='max')
logger = GenericDualMethodLogger(dual_method)
for iteration in range(10):
# print dual_method.lambda_k
# print dual_method.d_k
dual_method.dual_step()
# Method should end close to lambda*
np.testing.assert_allclose(logger.lambda_k_iterates[-1],
np.array([0.91, 1.]),
rtol=1e-2,
atol=0)
# with value close to dual optimum
np.testing.assert_allclose(logger.d_k_iterates[-1],
-0.54,
rtol=1e-2,
atol=0)
def test_DSA_on_analytical_example():
print('# Test Double Simple Averaging Method on Analytical Example')
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = AnalyticalExampleInnerProblem()
# it looks like lower gammas give faster convergence, but more oscillations
GAMMA = 0.5
dual_method = SGMDoubleSimpleAveraging(
analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension,
gamma=GAMMA,
sense='max')
logger = GenericDualMethodLogger(dual_method)
for iteration in range(20):
# print dual_method.lambda_k
# print dual_method.d_k
dual_method.dual_step()
# Method should end close to lambda*
# np.testing.assert_allclose(logger.lambda_k_iterates[-1], np.array([1., 1.]), rtol=1e-1, atol=0)
assert 0.95 <= logger.lambda_k_iterates[-1][
0] <= 1.05 # first coordinate should be ~1.0
assert 0.95 <= logger.lambda_k_iterates[-1][
1] <= 1.55 # second coordinate should be 1.0 <= coord <= 1.5
# with value close to dual optimum
np.testing.assert_allclose(logger.d_k_iterates[-1],
-0.5,
rtol=1e-1,
atol=0)
def test_subgradient_method_sanity_checks():
print('# Test Subgradient Method Sanity')
# ensure STEPSIZE_0 has defaults
# subgradient_method = SubgradientMethod('oracle', 'projection')
# custom STEPSIZE_0
subgradient_method = SubgradientMethod(mock_one_dim_oracle,
mock_projection_function,
dimension=1,
stepsize_0=1.5,
stepsize_rule='constant',
sense='max')
# logging
logger = GenericDualMethodLogger(subgradient_method)
# verify initial state
assert subgradient_method.lambda_k == 0
for iteration in range(3):
subgradient_method.dual_step()
# start: lambda_k = 0
# it 1: lambda_k = 1.95 = 0 + 1.5 (STEPSIZE_0) * 1.3 (diff_d_k from mock_oracle)
# it 2: lambda_k = 3.9 = 1.95 + 1.95
# it 3: lambda_k = 5.85
for iteration in range(3):
# default stepsize rule is 1/k
subgradient_method.dual_step()
# it 4: lambda_k = 6.3375 = 5.85 + (1.5/4) * 1.3
# etc.
print(subgradient_method.desc)
# verify final states with mock oracle
assert subgradient_method.x_k == 1.1
assert subgradient_method.d_k == 1.2
# print(logger.lambda_k_iterates)
np.testing.assert_allclose(
logger.lambda_k_iterates,
np.array([[0], [1.95], [3.9], [5.85], [7.8], [9.75]]), # [11.7]
atol=0.1)
def test_DSA_on_Bertsekas_example():
print('# DSA on Bertsekas Example')
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = BertsekasCounterExample()
# it looks like lower gammas give faster convergence, but more oscillations
GAMMA = 0.5
dual_method = SGMDoubleSimpleAveraging(
analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension,
gamma=0.5,
sense='max')
logger = GenericDualMethodLogger(dual_method)
# move initial point
lambda_0 = np.array([2, 2])
dual_method.lambda_k = lambda_0
for iteration in range(20):
# print(dual_method.lambda_k)
# print(dual_method.d_k)
dual_method.dual_step()
# print(logger.d_k_iterates)
# print(logger.lambda_k_iterates)
# Method should end close to lambda*
assert -3 <= logger.lambda_k_iterates[-1][
0] <= -2.2 # first coordinate should be ~3.0
assert 0 <= logger.lambda_k_iterates[-1][
1] <= 0.5 # second coordinate should be ~0
# with value close to dual optimum
np.testing.assert_allclose(logger.d_k_iterates[-1],
23.15,
rtol=1e-1,
atol=0)
def test_UPGM_on_second_analytical_example():
print('# Test UPGM on Second Analytical Example (1 eq, 1 ineq)')
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = SecondAnalyticalExampleInnerProblem()
dual_method = UniversalPGM(analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension,
epsilon=0.01)
logger = GenericDualMethodLogger(dual_method)
for iteration in range(5):
# print(dual_method.lambda_k)
# print(dual_method.d_k)
# print(logger.L_k_iterates)
dual_method.dual_step()
# Method should end close to lambda*
np.testing.assert_allclose(logger.lambda_k_iterates[-1],
np.array([1., 0.]),
atol=0.1)
# with value close to dual optimum
np.testing.assert_allclose(logger.d_k_iterates[-1], -1, rtol=1e-1, atol=0)