def test_get_hypergrid(self):
hyperparam_config = [HyperParameter(0, 4, 1), HyperParameter(0, 5, 2)]
grid = get_hypergrid(hyperparam_config)
target = np.array([[0., 0.], [0., 2.], [0., 4.], [1., 0.], [1., 2.],
[1., 4.], [2., 0.], [2., 2.], [2., 4.], [3., 0.],
[3., 2.], [3., 4.], [4., 0.], [4., 2.], [4., 4.]])
np.testing.assert_almost_equal(grid, target, decimal=5)
def test_prune_hypergrid(self):
hyperparam_config = [HyperParameter(0, 4, 1), HyperParameter(0, 5, 2)]
tested_points = np.array([[0, 4.0], [1, 0], [3, 2], [4, 2]])
fullgrid = get_hypergrid(hyperparam_config)
grid = prune_hypergrid(fullgrid, tested_points=tested_points)
target = np.array([[0., 0.], [0., 2.], [1., 2.], [1., 4.], [2., 0.],
[2., 2.], [2., 4.], [3., 0.], [3., 4.], [4., 0.],
[4., 4.]])
np.testing.assert_almost_equal(grid, target, decimal=5)
def minimize_function(function: Callable,
hyperparams_config: List[HyperParameter],
extra_function_args: Tuple = (),
tolerance: float = 1e-2,
max_iterations: int = 1000,
seed: int = None) -> Tuple[np.ndarray, float]:
"""
Find the minimum of a function
:param function: Function to be optimized. It will be called as ``f(x, *extra_function_args)``,
where ``x`` is the argument in the form of a 1-D array and ``extra_function_args``
is a tuple of any additional fixed parameters needed to completely specify the function.
:param hyperparams_config: List of hyperparameters
:param extra_function_args: Function is called as ``f(x, *extra_function_args)``
:param tolerance: Convergence tolerance, the optimization stops if (last_best_value - new_best_value) < tolerance
:param max_iterations: Maximum allowed number of iterations
:param seed: randomizer seed
:return:
- Solution (best point)
- Function value at best point
"""
if seed is not None:
np.random.seed(seed)
hypergrid = get_hypergrid(hyperparams_config)
tested_points = np.empty((0, len(hyperparams_config)))
tested_values = np.empty((0, 1))
maxvalue = hyperparams_config[0].upper_bound + 1
old_minimum = np.inf
num_points = 1
new_points = np.ones(
(num_points, len(hyperparams_config)), dtype=float) * maxvalue
if (len(hypergrid) < max_iterations):
max_iterations = len(hypergrid)
for idx in range(max_iterations):
hypergrid, new_points = _propose_new_points(new_points, hypergrid,
hyperparams_config,
num_points)
new_values = np.empty((num_points, 1))
for idx in range(num_points):
new_values[idx, 0] = function(new_points[idx, :],
*extra_function_args)
tested_points = np.concatenate((tested_points, new_points), axis=0)
tested_values = np.concatenate((tested_values, new_values), axis=0)
if np.abs(old_minimum - np.min(tested_values)) < tolerance:
break
best_point = np.argmin(tested_values, axis=0).item()
return tested_points[best_point], tested_values[best_point]
def test_get_new_unique_points_UCB(self):
hyperparam_config = [HyperParameter(0, 3, 1), HyperParameter(0, 5, 2)]
grid = get_hypergrid(hyperparam_config)
known_points = np.array([[0, 0]])
values = np.array([-2])
gp_settings = dict(kernel=rbf, kernel_params=(0.02, 0.25), noise=1e-6)
gp = GaussianProcessRegression(gp_settings["kernel"],
*gp_settings["kernel_params"],
noise=gp_settings["noise"])
gp.fit(known_points, values, grid)
ucb_tradeoff = 0.5
new_points = _get_new_unique_point_UCB(grid, gp, ucb_tradeoff)
target = np.array([[0., 0.]])
np.testing.assert_allclose(new_points, target, atol=1e-5)
def test_get_new_unique_points_Thompson(self):
hyperparam_config = [HyperParameter(0, 3, 1), HyperParameter(0, 5, 2)]
grid = get_hypergrid(hyperparam_config)
num_points = 5
gp_settings = dict(kernel=rbf, kernel_params=(0.02, 0.25), noise=1e-6)
gp = GaussianProcessRegression(gp_settings["kernel"],
*gp_settings["kernel_params"],
noise=gp_settings["noise"])
gp.initialize(grid)
new_points = _get_new_unique_points_Thompson(grid, gp, num_points)
for i in range(len(new_points)):
for j in range(i + 1, len(new_points)):
self.assertFalse(np.array_equal(new_points[i], new_points[j]))
def test_get_new_unique_point(self):
hyperparam_config = [
HyperParameter(0, 4, 1),
HyperParameter(0, 5, 2)
]
grid = get_hypergrid(hyperparam_config)
previous_points = np.array([
[0, 4],
[1, 0],
[3, 2],
[4, 2]
])
for idx in range(100):
self.assertTrue(not_in_array(_get_new_unique_point(previous_points, grid, 100), previous_points))
# Check error
with self.assertRaises(OptimizerError):
_get_new_unique_point(previous_points, previous_points)
def test_get_new_unique_point_Thompson(self):
hyperparam_config = [HyperParameter(0, 3, 1), HyperParameter(0, 5, 2)]
grid = get_hypergrid(hyperparam_config)
previous_points = np.array([[0, 4], [1, 0], [3, 2], [4, 2]])
gp_settings = dict(kernel=rbf, kernel_params=(0.02, 0.25), noise=1e-6)
gp = GaussianProcessRegression(gp_settings["kernel"],
*gp_settings["kernel_params"],
noise=gp_settings["noise"])
gp.initialize(grid)
for idx in range(100):
self.assertTrue(
not_in_array(
_get_single_point_Thompson(previous_points, grid, gp, 100),
previous_points))
# Check error
gp.initialize(previous_points)
with self.assertRaises(OptimizerError):
_get_single_point_Thompson(previous_points, previous_points, gp)
def propose_points(tested_points: np.ndarray,
tested_values: np.ndarray,
hyperparams_config: List[HyperParameter],
num_points: int,
seed: int = None,
acquisition_function: str = "Thompson",
gp_settings: Dict = None) -> np.ndarray:
"""
Propose new points to test based on past values. The proposed points should leaad function minimum values
:param tested_points: previously tested points with dims (n_points, n_hyperparameters)
:param tested_values: List of function values for previously tested points dims: (n_points, 1)
:param hyperparams_config: List of hyperparameters
:param num_points: number of points to propose
:param seed: randomizer seed
:param acquisition_function: "Thompson" for thompson sampling or "UCB" for Upper condence bound
:param gp_settings: settings for the GaussianProcessRegressor: kernel, kernel_params and noise
:return: New points to test with dims (num_points, n_hyperparameters)
"""
if seed is not None:
np.random.seed(seed)
if gp_settings is None:
gp_settings = dict(kernel=rbf, kernel_params=(0.1, 1), noise=1e-6)
gp = GaussianProcessRegression(gp_settings["kernel"],
*gp_settings["kernel_params"],
noise=gp_settings["noise"])
hypergrid = get_hypergrid(hyperparams_config)
hypergrid, new_points = _propose_new_points(tested_points, tested_points,
tested_values, hypergrid,
hyperparams_config, num_points,
acquisition_function,
gp_settings)
return new_points
def propose_points(tested_points: np.ndarray,
tested_values: np.ndarray,
hyperparams_config: List[HyperParameter],
num_points: int,
seed: int = None) -> np.ndarray:
"""
Propose new points to test based on past values
:param tested_points: previously tested points with dims (n_points, n_hyperparameters)
:param tested_values: List of function values for previously tested points dims: (n_points, 1)
:param hyperparams_config: List of hyperparameters
:param num_points: number of points to propose
:param seed: randomizer seed
:return: New points to test with dims (num_points, n_hyperparameters)
"""
if seed is not None:
np.random.seed(seed)
hypergrid = get_hypergrid(hyperparams_config)
hypergrid, new_points = _propose_new_points(tested_points, hypergrid,
hyperparams_config, num_points)
return new_points
def minimize_function(function: Callable,
hyperparams_config: List[HyperParameter],
extra_function_args: Tuple = (),
tolerance: float = 1e-2,
max_iterations: int = 1000,
seed: int = None,
acquisition_function: str = "UCB",
gp_settings: Dict = None) -> Tuple[np.ndarray, float]:
"""
Find the minimum of a function
:param function: Function to be optimized. It will be called as ``f(x, *extra_function_args)``,
where ``x`` is the argument in the form of a 1-D array and ``extra_function_args``
is a tuple of any additional fixed parameters needed to completely specify the function.
:param hyperparams_config: List of hyperparameters
:param extra_function_args: Function is called as ``f(x, *extra_function_args)``
:param tolerance: Convergence tolerance, the optimization stops if (last_best_value - new_best_value) < tolerance
:param max_iterations: Maximum allowed number of iterations
:param seed: randomizer seed
:param acquisition_function: "Thompson" for thompson sampling or "UCB" for Upper condence bound
:param gp_settings: settings for the GaussianProcessRegressor: kernel, kernel_params and noise
:return:
- Solution (best point)
- Function value at best point
"""
if seed is not None:
np.random.seed(seed)
if gp_settings is None:
gp_settings = dict(kernel=rbf, kernel_params=(0.1, 1), noise=1e-6)
# ------ Define the initial grid
hypergrid = get_hypergrid(hyperparams_config)
tested_points = np.empty((0, len(hyperparams_config)))
tested_values = np.empty((0, 1))
maxvalue = hyperparams_config[0].upper_bound + 1
# ------ Define useful constants
old_minimum = np.inf
num_points = 1
new_points = np.empty((0, len(hyperparams_config)))
max_iterations = min(len(hypergrid), max_iterations)
stopping_counter = 0
for idx in range(max_iterations):
# ------ Ask the optimizer for new points
hypergrid, new_points = _propose_new_points(
new_points, tested_points, tested_values, hypergrid,
hyperparams_config, num_points, acquisition_function, gp_settings)
new_values = np.empty((num_points, 1))
for idx in range(num_points):
new_values[idx, 0] = function(new_points[idx, :],
*extra_function_args)
tested_points = np.concatenate((tested_points, new_points), axis=0)
tested_values = np.concatenate((tested_values, new_values), axis=0)
# ------ Compute the stopping criterion
if np.abs(old_minimum - np.min(tested_values)) < tolerance:
stopping_counter += 1
else:
stopping_counter = 0
if stopping_counter >= 10:
break
old_minimum = np.min(tested_values)
best_point = np.argmin(tested_values, axis=0).item()
return tested_points[best_point], tested_values[best_point]
