def test_barrier_one_step():
# Simple 2-dimensional problem with identity matrix.
A = np.eye(2)
b = np.array([1.0, 0.0])
reg_coef = 1.0
x_0 = np.array([0.0, 1.0])
u_0 = np.array([2.0, 2.0])
(x_star, u_star), message, history = optimization.barrier_method_lasso(
A, b, reg_coef, x_0, u_0,
lasso_duality_gap=oracles.lasso_duality_gap,
trace=True)
eq_(message, "success")
ok_(np.allclose(
x_star,
np.array([0.00315977, 0.0])))
ok_(isinstance(x_star, np.ndarray))
ok_(np.allclose(
u_star,
np.array([3.16979051e-03, 2.00000000e-05])))
ok_(isinstance(u_star, np.ndarray))
check_equal_histories(
history,
{'time': [None] * 7,
'duality_gap': [
2.0,
0.47457244767635376,
0.083152839863428252,
0.0094880329978710432,
0.0009840651705023129,
9.9498755346316692e-05,
9.9841761475039092e-06]})
def test_barrier_univariate():
# Minimize 1/2 * x^2 + 3.0 * u,
# s.t. -u <= x <= u
A = np.array([[1.0]])
b = np.array([0.0])
reg_coef = 3.0
x_0 = np.array([1.0])
u_0 = np.array([2.0])
print("Univariate")
(x_star, u_star), message, history = optimization.barrier_method_lasso(
A, b, reg_coef, x_0, u_0,
lasso_duality_gap=oracles.lasso_duality_gap,
trace=True)
eq_(message, "success")
ok_(np.allclose(
x_star,
np.array([-7.89796404e-07])))
ok_(isinstance(x_star, np.ndarray))
ok_(np.allclose(
u_star,
np.array([0.66666568])))
ok_(isinstance(u_star, np.ndarray))
check_equal_histories(
history,
{'time': [None] * 2,
'duality_gap': [4.0, 2.3693898355252885e-06]})
def experiment_2(parameter='n', seed=31415):
# n, m and lambda
n, m, reg_coef = 500, 500, 1.0
np.random.seed(seed)
grids = dict()
grids['n'] = [10, 100, 500, 1000, 2000]
grids['m'] = [10, 100, 500, 1000, 2000]
grids['reg_coef'] = [0.01, 0.1, 1.0, 10.0, 100.0]
fig1, ax1 = plt.subplots()
fig2, ax2 = plt.subplots()
ax1.set_xlabel('Номер итерации')
ax1.set_ylabel('Гарантированная точность по зазору двойственности')
ax1.grid()
ax1.set_yscale('log')
ax2.set_xlabel('Время от начала эксперимента')
ax2.set_ylabel('Гарантированная точность по зазору двойственности')
ax2.grid()
ax2.set_yscale('log')
os.makedirs("report/pics/2", exist_ok=True)
experiment_parameters = {'n': n, 'm': m, 'reg_coef': 1.0}
for value in grids[parameter]:
experiment_parameters[parameter] = value
A = np.random.randn(experiment_parameters['m'],
experiment_parameters['n'])
b = np.random.randn(experiment_parameters['m'])
# x_0 = np.zeros(experiment_parameters['n'])
x_0 = 0.1 * np.ones(experiment_parameters['n'])
u_0 = 2 * x_0
reg_coef = experiment_parameters['reg_coef']
(x_opt, u_opt), message, history = barrier_method_lasso(
A,
b,
reg_coef,
x_0=x_0,
u_0=u_0,
lasso_duality_gap=lasso_duality_gap,
trace=True)
ax1.plot(history['duality_gap'], label=f'{parameter}={value}')
ax2.plot(history['time'],
history['duality_gap'],
label=f'{parameter}={value}')
ax1.legend()
ax2.legend()
os.makedirs("report/pics/2", exist_ok=True)
fig1.savefig(f"report/pics/2/barrier_lasso_gap_vs_iter_{parameter}.pdf",
bbox_inches='tight')
fig2.savefig(f"report/pics/2/barrier_lasso_gap_vs_time_{parameter}.pdf",
bbox_inches='tight')
def experiment_1(parameter='gamma'):
# gamma and eps_inner
np.random.seed(31415)
data_path = "data"
datasets = ["abalone", "cpusmall", "housing", "triazines"]
gamma_grid = [2, 10, 100, 1000]
inner_eps_grid = [1e-8, 1e-6, 1e-4, 1e-2, 1e-1, 5e-1]
for dataset in datasets:
fig1, ax1 = plt.subplots()
fig2, ax2 = plt.subplots()
ax1.set_xlabel('Номер итерации')
ax1.set_ylabel('Гарантированная точность по зазору двойственности')
ax1.grid()
ax1.set_yscale('log')
ax2.set_xlabel('Время от начала эксперимента')
ax2.set_ylabel('Гарантированная точность по зазору двойственности')
ax2.grid()
ax2.set_yscale('log')
print("___________________________")
logging.info(f"{dataset} is in process...")
A, b = load_svmlight_file(os.path.join(data_path, dataset))
print(A.shape, 1 - A.size / (A.shape[0] * A.shape[1]),
np.linalg.matrix_rank(A.toarray()))
os.makedirs("report/pics/1", exist_ok=True)
n = A.shape[1]
x0 = np.zeros(n)
u0 = 0.1 * np.ones(n)
# x0 = np.random.randn(n)
# u0 = np.abs(x0) * 2
if parameter == 'gamma':
for gamma in gamma_grid:
(x_opt, u_opt), message, history = barrier_method_lasso(
A,
b,
1.0,
x0,
u0,
gamma=gamma,
lasso_duality_gap=lasso_duality_gap,
trace=True)
ax1.plot(history['duality_gap'], label=f'gamma={gamma}')
ax2.plot(history['time'],
history['duality_gap'],
label=f'gamma={gamma}')
else:
for inner_eps in inner_eps_grid:
(x_opt, u_opt), message, history = barrier_method_lasso(
A,
b,
1.0,
np.zeros(n),
np.ones(n),
tolerance_inner=inner_eps,
lasso_duality_gap=lasso_duality_gap,
trace=True)
ax1.plot(history['duality_gap'],
label=f'eps_inner={inner_eps}')
ax2.plot(history['time'],
history['duality_gap'],
label=f'eps_inner={inner_eps}')
ax1.legend()
ax2.legend()
os.makedirs("report/pics/1", exist_ok=True)
fig1.savefig(
f"report/pics/1/barrier_lasso_gap_vs_iter_{parameter}_{dataset}.pdf",
bbox_inches='tight')
fig2.savefig(
f"report/pics/1/barrier_lasso_gap_vs_time_{parameter}_{dataset}.pdf",
bbox_inches='tight')