def test_bundle_method_on_analytical_example():
print('# Test Bundle Method on Analytical Example (2 ineq)')
# see definition of AnalyticalExampleInnerProblem for problem and solution statement
analytical_inner_problem = AnalyticalExampleInnerProblem()
dual_method = BundleMethod(analytical_inner_problem.oracle,
analytical_inner_problem.projection_function,
dimension=analytical_inner_problem.dimension,
epsilon=0.01,
sense='max')
dual_method.set_dual_domain(type='positive orthant', param=0.5)
logger = EnhancedDualMethodLogger(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* = [1, [1-1.5]]
# np.testing.assert_allclose(logger.lambda_k_iterates[-1], np.array([1, 1.5]), atol=0.01)
lambda_star = logger.lambda_k_iterates[-1]
assert abs(lambda_star[0] - 1) <= 0.01
assert lambda_star[1] >= 0.99
assert lambda_star[1] <= 1.51
# with value close to dual optimum d*=-1
np.testing.assert_allclose(logger.d_k_iterates[-1], -0.5, atol=0.02)
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_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_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)