#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
from collections import defaultdict
from typing import TYPE_CHECKING, Callable, Dict, List, Optional, Set, Tuple, Union
import numpy as np
import torch
from ax.core.types import TConfig, TParamCounter
from ax.models.torch_base import TorchModel
if TYPE_CHECKING:
# import as module to make sphinx-autodoc-typehints happy
from ax import models # noqa F401 # pragma: no cover
Tensoray = Union[torch.Tensor, np.ndarray]
DEFAULT_MAX_RS_DRAWS = 10000
[docs]def rejection_sample(
gen_unconstrained: Callable[
[int, int, np.ndarray, Optional[Dict[int, float]]], np.ndarray
],
n: int,
d: int,
tunable_feature_indices: np.ndarray,
linear_constraints: Optional[Tuple[np.ndarray, np.ndarray]] = None,
deduplicate: bool = False,
max_draws: Optional[int] = None,
fixed_features: Optional[Dict[int, float]] = None,
rounding_func: Optional[Callable[[np.ndarray], np.ndarray]] = None,
existing_points: Optional[np.ndarray] = None,
) -> Tuple[np.ndarray, int]:
"""Rejection sample in parameter space.
Models must implement a `gen_unconstrained` method in order to support
rejection sampling via this utility.
"""
# We need to perform the round trip transformation on our generated point
# in order to deduplicate in the original search space.
# The transformation is applied above.
if deduplicate and rounding_func is None:
raise ValueError(
"Rounding function must be provided for deduplication." # pragma: no cover
)
failed_constraint_dict: TParamCounter = defaultdict(lambda: 0)
# Rejection sample with parameter constraints.
points = np.zeros((n, d))
attempted_draws = 0
successful_draws = 0
if max_draws is None:
max_draws = DEFAULT_MAX_RS_DRAWS
while successful_draws < n and attempted_draws <= max_draws:
# _gen_unconstrained returns points including fixed features.
# pyre-ignore: Anonymous function w/ named args.
point = gen_unconstrained(
n=1,
d=d,
tunable_feature_indices=tunable_feature_indices,
fixed_features=fixed_features,
)[0]
# Note: this implementation may not be performant, if the feasible volume
# is small, since applying the rounding_func is relatively expensive.
# If sampling in spaces with low feasible volume is slow, this function
# could be applied after checking the linear constraints.
if rounding_func is not None:
point = rounding_func(point)
# Check parameter constraints, always in raw transformed space.
if linear_constraints is not None:
all_constraints_satisfied, violators = check_param_constraints(
linear_constraints=linear_constraints, point=point
)
for violator in violators:
failed_constraint_dict[violator] += 1
else:
all_constraints_satisfied = True
violators = np.array([])
# Deduplicate: don't add the same point twice.
duplicate = False
if deduplicate:
if existing_points is not None:
prev_points = np.vstack([points, existing_points])
else:
prev_points = points
duplicate = check_duplicate(point=point, points=prev_points)
# Add point if valid.
if all_constraints_satisfied and not duplicate:
points[successful_draws] = point
successful_draws += 1
attempted_draws += 1
if successful_draws < n:
# Only possible if attempted_draws >= max_draws.
raise ValueError(
f"Specified maximum draws ({max_draws}) exhausted, without "
f"finding sufficiently many ({n}) candidates."
)
else:
return (points, attempted_draws)
[docs]def check_duplicate(point: np.ndarray, points: np.ndarray) -> bool:
"""Check if a point exists in another array.
Args:
point: Newly generated point to check.
prev_points: Points previously generated.
Returns:
True if the point is contained in points, else False
"""
return np.any(np.isin(points, point).all(axis=1))
[docs]def add_fixed_features(
tunable_points: np.ndarray,
d: int,
fixed_features: Optional[Dict[int, float]],
tunable_feature_indices: np.ndarray,
) -> np.ndarray:
"""Add fixed features to points in tunable space.
Args:
tunable_points: Points in tunable space.
d: Dimension of parameter space.
fixed_features: A map {feature_index: value} for features that
should be fixed to a particular value during generation.
tunable_feature_indices: Parameter indices (in d) which are tunable.
Returns:
points: Points in the full d-dimensional space, defined by bounds.
"""
n = np.shape(tunable_points)[0]
points = np.zeros((n, d))
points[:, tunable_feature_indices] = tunable_points
if fixed_features:
fixed_feature_indices = np.array(list(fixed_features.keys()))
fixed_values = np.tile(list(fixed_features.values()), (n, 1))
points[:, fixed_feature_indices] = fixed_values
return points
[docs]def check_param_constraints(
linear_constraints: Tuple[np.ndarray, np.ndarray], point: np.ndarray
) -> Tuple[bool, np.ndarray]:
"""Check if a point satisfies parameter constraints.
Args:
linear_constraints: A tuple of (A, b). For k linear constraints on
d-dimensional x, A is (k x d) and b is (k x 1) such that
A x <= b.
point: A candidate point in d-dimensional space, as a (1 x d) matrix.
Returns:
2-element tuple containing
- Flag that is True if all constraints are satisfied by the point.
- Indices of constraints which are violated by the point.
"""
constraints_satisfied = (
linear_constraints[0] @ np.expand_dims(point, axis=1) <= linear_constraints[1]
)
if np.all(constraints_satisfied):
return True, np.array([])
else:
return (False, np.where(constraints_satisfied == False)[0]) # noqa: E712
[docs]def tunable_feature_indices(
bounds: List[Tuple[float, float]], fixed_features: Optional[Dict[int, float]] = None
) -> np.ndarray:
"""Get the feature indices of tunable features.
Args:
bounds: A list of (lower, upper) tuples for each column of X.
fixed_features: A map {feature_index: value} for features that
should be fixed to a particular value during generation.
Returns:
The indices of tunable features.
"""
fixed_feature_indices = list(fixed_features.keys()) if fixed_features else []
feature_indices = np.arange(len(bounds))
return np.delete(feature_indices, fixed_feature_indices)
[docs]def validate_bounds(
bounds: List[Tuple[float, float]], fixed_feature_indices: np.ndarray
) -> None:
"""Ensure the requested space is [0,1]^d.
Args:
bounds: A list of d (lower, upper) tuples for each column of X.
fixed_feature_indices: Indices of features which are fixed at a
particular value.
"""
for feature_idx, bound in enumerate(bounds):
# Bounds for fixed features are not unit-transformed.
if feature_idx in fixed_feature_indices:
continue
if bound[0] != 0 or bound[1] != 1:
raise ValueError(
"This generator operates on [0,1]^d. Please make use "
"of the UnitX transform in the ModelBridge, and ensure "
"task features are fixed."
)
[docs]def best_observed_point(
model: Union["models.numpy_base.NumpyModel", "models.torch_base.TorchModel"],
bounds: List[Tuple[float, float]],
objective_weights: Optional[Tensoray],
outcome_constraints: Optional[Tuple[Tensoray, Tensoray]] = None,
linear_constraints: Optional[Tuple[Tensoray, Tensoray]] = None,
fixed_features: Optional[Dict[int, float]] = None,
options: Optional[TConfig] = None,
) -> Optional[np.ndarray]:
"""Select the best point that has been observed.
Implements two approaches to selecting the best point.
For both approaches, only points that satisfy parameter space constraints
(bounds, linear_constraints, fixed_features) will be returned. Points must
also be observed for all objective and constraint outcomes. Returned
points may violate outcome constraints, depending on the method below.
1: Select the point that maximizes the expected utility
(objective_weights^T posterior_objective_means - baseline) * Prob(feasible)
Here baseline should be selected so that at least one point has positive
utility. It can be specified in the options dict, otherwise
min (objective_weights^T posterior_objective_means)
will be used, where the min is over observed points.
2: Select the best-objective point that is feasible with at least
probability p.
The following quantities may be specified in the options dict:
- best_point_method: 'max_utility' (default) or 'feasible_threshold'
to select between the two approaches described above.
- utility_baseline: Value for the baseline used in max_utility approach. If
not provided, defaults to min objective value.
- probability_threshold: Threshold for the feasible_threshold approach.
Defaults to p=0.95.
- feasibility_mc_samples: Number of MC samples used for estimating the
probability of feasibility (defaults 10k).
Args:
model: Numpy or Torch model.
bounds: A list of (lower, upper) tuples for each feature.
objective_weights: The objective is to maximize a weighted sum of
the columns of f(x). These are the weights.
outcome_constraints: A tuple of (A, b). For k outcome constraints
and m outputs at f(x), A is (k x m) and b is (k x 1) such that
A f(x) <= b.
linear_constraints: A tuple of (A, b). For k linear constraints on
d-dimensional x, A is (k x d) and b is (k x 1) such that
A x <= b.
fixed_features: A map {feature_index: value} for features that
should be fixed to a particular value in the best point.
options: A config dictionary with settings described above.
Returns:
A d-array of the best point, or None if no feasible point exists.
"""
if not hasattr(model, "Xs"):
raise ValueError(f"Model must store training data Xs, but {model} does not.")
# Parse options
if options is None:
options = {}
method: str = options.get("best_point_method", "max_utility")
B: Optional[float] = options.get("utility_baseline", None)
threshold: float = options.get("probability_threshold", 0.95)
nsamp: int = options.get("feasibility_mc_samples", 10000)
# Get points observed for all objective and constraint outcomes
if objective_weights is None:
return None # pragma: no cover
objective_weights_np = as_array(objective_weights)
X_obs = get_observed(
# pyre-fixme[16]: attribute must exist, otherwise error raised above
Xs=model.Xs,
objective_weights=objective_weights,
outcome_constraints=outcome_constraints,
)
# Filter to those that satisfy constraints.
X_obs = filter_constraints_and_fixed_features(
X=X_obs,
bounds=bounds,
linear_constraints=linear_constraints,
fixed_features=fixed_features,
)
if len(X_obs) == 0:
# No feasible points
return None
# Predict objective and P(feas) at these points
if isinstance(model, TorchModel):
# pyre-fixme[29]: `Union[() -> Tensor, Any]` is not a function.
X_obs = X_obs.clone().detach()
f, cov = as_array(model.predict(X_obs))
obj = objective_weights_np @ f.transpose() # pyre-ignore
pfeas = np.ones_like(obj)
if outcome_constraints is not None:
A, b = as_array(outcome_constraints) # (m x j) and (m x 1)
# Use Monte Carlo to compute pfeas, to properly handle covariance
# across outcomes.
for i, _ in enumerate(X_obs):
z = np.random.multivariate_normal(
mean=f[i, :], cov=cov[i, :, :], size=nsamp
) # (nsamp x j)
pfeas[i] = (A @ z.transpose() <= b).all(axis=0).mean()
# Identify best point
if method == "feasible_threshold":
utility = obj
utility[pfeas < threshold] = -np.Inf
elif method == "max_utility":
if B is None:
B = obj.min()
utility = (obj - B) * pfeas
i = np.argmax(utility)
if utility[i] == -np.Inf:
return None
else:
return X_obs[i, :]
[docs]def as_array(
x: Union[Tensoray, Tuple[Tensoray, ...]]
) -> Union[np.ndarray, Tuple[np.ndarray, ...]]:
"""Convert every item in a tuple of tensors/arrays into an array.
Args:
x: A tensor, array, or a tuple of potentially mixed tensors and arrays.
Returns:
x, with everything converted to array.
"""
if isinstance(x, tuple):
return tuple(as_array(x_i) for x_i in x) # pyre-ignore
elif isinstance(x, np.ndarray):
return x
elif torch.is_tensor(x):
return x.detach().cpu().double().numpy()
else:
raise ValueError(
"Input to as_array must be numpy array or torch tensor"
) # pragma: no cover
[docs]def get_observed(
Xs: Union[List[torch.Tensor], List[np.ndarray]],
objective_weights: Tensoray,
outcome_constraints: Optional[Tuple[Tensoray, Tensoray]] = None,
) -> Tensoray:
"""Filter points to those that are observed for objective outcomes and outcomes
that show up in outcome_constraints (if there are any).
Args:
Xs: A list of m (k_i x d) feature matrices X. Number of rows k_i
can vary from i=1,...,m.
objective_weights: The objective is to maximize a weighted sum of
the columns of f(x). These are the weights.
outcome_constraints: A tuple of (A, b). For k outcome constraints
and m outputs at f(x), A is (k x m) and b is (k x 1) such that
A f(x) <= b.
Returns:
Points observed for all objective outcomes and outcome constraints.
"""
objective_weights_np = as_array(objective_weights)
used_outcomes: Set[int] = set(np.where(objective_weights_np != 0)[0])
if len(used_outcomes) == 0:
raise ValueError("At least one objective weight must be non-zero")
if outcome_constraints is not None:
used_outcomes = used_outcomes.union(
np.where(as_array(outcome_constraints)[0] != 0)[1]
)
outcome_list = list(used_outcomes)
X_obs_set = {tuple(float(x_i) for x_i in x) for x in Xs[outcome_list[0]]}
for _, idx in enumerate(outcome_list, start=1):
X_obs_set = X_obs_set.intersection(
{tuple(float(x_i) for x_i in x) for x in Xs[idx]}
)
if isinstance(Xs[0], np.ndarray):
return np.array(list(X_obs_set), dtype=Xs[0].dtype) # (n x d)
if isinstance(Xs[0], torch.Tensor):
return torch.tensor(list(X_obs_set), device=Xs[0].device, dtype=Xs[0].dtype)
[docs]def filter_constraints_and_fixed_features(
X: Tensoray,
bounds: List[Tuple[float, float]],
linear_constraints: Optional[Tuple[Tensoray, Tensoray]] = None,
fixed_features: Optional[Dict[int, float]] = None,
) -> Tensoray:
"""Filter points to those that satisfy bounds, linear_constraints, and
fixed_features.
Args:
X: An tensor or array of points.
bounds: A list of (lower, upper) tuples for each feature.
linear_constraints: A tuple of (A, b). For k linear constraints on
d-dimensional x, A is (k x d) and b is (k x 1) such that
A x <= b.
fixed_features: A map {feature_index: value} for features that
should be fixed to a particular value in the best point.
Returns:
Feasible points.
"""
if len(X) == 0: # if there are no points, nothing to filter
return X
X_np = X
if isinstance(X, torch.Tensor):
X_np = X.cpu().numpy()
feas = np.ones(X_np.shape[0], dtype=bool) # (n)
for i, b in enumerate(bounds):
feas &= (X_np[:, i] >= b[0]) & (X_np[:, i] <= b[1])
if linear_constraints is not None:
A, b = as_array(linear_constraints) # (m x d) and (m x 1)
feas &= (A @ X_np.transpose() <= b).all(axis=0)
if fixed_features is not None:
for idx, val in fixed_features.items():
feas &= X_np[:, idx] == val
X_feas = X_np[feas, :]
if isinstance(X, torch.Tensor):
return torch.from_numpy(X_feas).to(device=X.device, dtype=X.dtype)
else:
return X_feas
