def test_history(self):
x0 = -np.array([1.3, 2.7])
opt = BFGS(self.oracle,
x0,
line_search_options={
'method': 'Constant',
'c': 1.0
},
tolerance=1e-6)
opt.run(10)
x_min = opt.hist['x_star']
func_steps = [25.635000000000005, 22.99, -9.48707349065929, -9.5]
grad_norm_steps = [11.629703349613008, 11.4, 0.22738961577617722, 0.0]
time_steps = [0.0] * 4 # Dummy values
x_steps = [
np.array([-1.3, -2.7]),
np.array([1.0, 8.7]),
np.array([1.0, 2.88630519]),
np.array([1., 3.])
]
true_history = dict(grad_norm=grad_norm_steps,
time=time_steps,
x=x_steps,
func=func_steps)
check_equal_histories(opt.hist, true_history)
def test_quality(self):
opt = BFGS(self.oracle, self.x0, tolerance=1e-5)
opt.run(5)
x_min = opt.hist['x_star']
# x_min, message, _ = LBFGS(self.oracle, self.x0, tolerance=1e-5)
f_min = self.oracle.func(x_min)
g_k_norm_sqr = norm(self.A.dot(x_min) - self.b, 2)**2
g_0_norm_sqr = norm(self.A.dot(self.x0) - self.b, 2)**2
self.assertLessEqual(g_k_norm_sqr, 1e-5 * g_0_norm_sqr)
self.assertLessEqual(abs(f_min - self.f_star), 1e-5 * g_0_norm_sqr)
def test_default(self):
"""Check if everything works correctly with default parameters."""
opt = BFGS(self.oracle, self.x0)
opt.run()
def test_max_iter(self):
"""Check if argument `max_iter` is supported."""
opt = BFGS(self.oracle, self.x0)
opt.run(max_iter=0)
def run_all_methods(oracle,
sketch_sizes,
mat,
max_iter,
output_folder,
x_0=None,
sigma_tolerance=1e-10,
method_tolerance=1e-16,
stopping_criteria='func_abs',
add_text='',
random_state=None,
linesearch_methods=['Wolfe'],
methods=None,
overwrite=False):
import os
os.system('mkdir -p {}'.format(output_folder))
if methods is None:
methods = ['svd', 'svd-no-sigma', 'gauss', 'coord', 'bfgs', 'nesterov']
np.random.seed(random_state)
if x_0 is None:
x_0 = np.random.normal(loc=0., scale=1., size=mat.shape[1])
add_text = '_{}'.format(add_text) if add_text != '' else ''
def run_rbfgs(mat_distr, line_search_options, distr_name, **kwargs):
output_file = '{}/rbfgs_{}_linesearch={}{}.pkl'.format(
output_folder, distr_name, line_search_options['method'].lower(),
add_text)
run_rbfgs_experiment(oracle,
x_0,
mat_distr=mat_distr,
sketch_sizes=sketch_sizes,
max_iter=max_iter,
tolerance=method_tolerance,
stopping_criteria=stopping_criteria,
output_file=output_file,
overwrite=overwrite,
**kwargs)
if 'svd' in methods or 'svd-no-sigma' in methods:
try:
with open('{}/svd.pkl'.format(output_folder), 'rb') as file:
U, sigma_diag, Vh = pickle.load(file)
print('Read SVD from {}/svd.pkl'.format(output_folder))
except FileNotFoundError:
print('Computing SVD...', end='')
U, sigma_diag, Vh = scipy.linalg.svd(mat.T, full_matrices=False)
print('Done')
with open('{}/svd.pkl'.format(output_folder), 'wb') as file:
pickle.dump((U, sigma_diag, Vh), file)
nondeg_count = (sigma_diag > sigma_tolerance).sum()
print('Singular values above tolerance: {}'.format(nondeg_count))
print()
if 'svd' in methods:
print('RBFGS-SVD sketch... ', end='')
mat_distr = CustomDiscrete(U[:, :nondeg_count], sort_ids=True)
for ls in linesearch_methods:
run_rbfgs(mat_distr, {'method': ls}, 'svd')
print('Done')
if 'svd-no-sigma' in methods:
print('RBFGS-SVD sketch no sigma... ', end='')
mat_distr = CustomDiscrete(U, sort_ids=True)
for ls in linesearch_methods:
run_rbfgs(mat_distr, {'method': ls}, 'svd-no-sigma')
print('Done')
if 'gauss' in methods:
print('RBFGS-gauss... ', end='')
mat_distr = Gaussian(-1., 1., [mat.shape[1], 1])
for ls in linesearch_methods:
run_rbfgs(mat_distr, {'method': ls}, 'gauss')
print('Done')
if 'coord' in methods:
print('RBFGS-coord...', end='')
mat_distr = CustomDiscrete(np.eye(mat.shape[1]), sort_ids=True)
for ls in linesearch_methods:
run_rbfgs(mat_distr, {'method': ls}, 'coord')
print('Done')
if 'bfgs' in methods:
print('BFGS... ', end='')
for ls in linesearch_methods:
if 'bfgs_linesearch={}{}.pkl'\
.format(ls.lower(), add_text) not in os.listdir(output_folder):
method = BFGS(oracle,
x_0,
tolerance=method_tolerance,
stopping_criteria=stopping_criteria,
line_search_options={'method': 'Wolfe'})
method.run(max_iter)
method.oracle = None
method.H_k = None
method.x_0 = None
with open('{}/bfgs_linesearch={}{}.pkl'\
.format(output_folder, ls.lower(), add_text), 'wb') as file:
pickle.dump(method, file)
print('Done')
print()
print('All runs completed.')