Source code for botorch.utils.feasible_volume

#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.

from __future__ import annotations

from typing import Callable, List, Optional, Tuple

import botorch.models.model as model
import torch
from torch import Tensor

from ..logging import _get_logger
from .sampling import manual_seed


logger = _get_logger(name="Feasibility")


[docs]def get_feasible_samples( samples: Tensor, inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None, ) -> Tuple[Tensor, float]: r""" Checks which of the samples satisfy all of the inequality constraints. Args: samples: A `sample size x d` size tensor of feature samples, where d is a feature dimension. inequality constraints: A list of tuples (indices, coefficients, rhs), with each tuple encoding an inequality constraint of the form `\sum_i (X[indices[i]] * coefficients[i]) >= rhs`. Returns: 2-element tuple containing - Samples satisfying the linear constraints. - Estimated proportion of samples satisfying the linear constraints. """ if inequality_constraints is None: return samples, 1.0 nsamples = samples.size(0) feasible = torch.ones(nsamples, device=samples.device, dtype=torch.bool) for (indices, coefficients, rhs) in inequality_constraints: lhs = samples.index_select(1, indices) @ coefficients.to(dtype=samples.dtype) feasible &= lhs >= rhs feasible_samples = samples[feasible] p_linear = feasible_samples.size(0) / nsamples return feasible_samples, p_linear
[docs]def get_outcome_feasibility_probability( model: model.Model, X: Tensor, outcome_constraints: List[Callable[[Tensor], Tensor]], threshold: float = 0.1, nsample_outcome: int = 1000, seed: Optional[int] = None, ) -> float: r""" Monte Carlo estimate of the feasible volume with respect to the outcome constraints. Args: model: The model used for sampling the posterior. X: A tensor of dimension `batch-shape x 1 x d`, where d is feature dimension. outcome_constraints: A list of callables, each mapping a Tensor of dimension `sample_shape x batch-shape x q x m` to a Tensor of dimension `sample_shape x batch-shape x q`, where negative values imply feasibility. threshold: A lower limit for the probability of posterior samples feasibility. nsample_outcome: The number of samples from the model posterior. seed: The seed for the posterior sampler. If omitted, use a random seed. Returns: Estimated proportion of features for which posterior samples satisfy given outcome constraints with probability above or equal to the given threshold. """ if outcome_constraints is None: return 1.0 from botorch.sampling import SobolQMCNormalSampler seed = seed if seed is not None else torch.randint(0, 1000000, (1,)).item() posterior = model.posterior(X) # posterior consists of batch_shape marginals sampler = SobolQMCNormalSampler(num_samples=nsample_outcome, seed=seed) # size of samples: (num outcome samples, batch_shape, 1, outcome dim) samples = sampler(posterior) feasible = torch.ones(samples.shape[:-1], dtype=torch.bool, device=samples.device) # a sample passes if each constraint applied to the sample # produces a non-negative tensor for oc in outcome_constraints: # broadcasted evaluation of the outcome constraints feasible &= oc(samples) <= 0 # proportion of feasibile samples for each of the elements of X # summation is done across feasible outcome samples p_feas = feasible.sum(0).float() / feasible.size(0) # proportion of features leading to the posterior outcome # satisfying the given outcome constraints # with at probability above a given threshold p_outcome = (p_feas >= threshold).sum().item() / X.size(0) return p_outcome
[docs]def estimate_feasible_volume( bounds: Tensor, model: model.Model, outcome_constraints: List[Callable[[Tensor], Tensor]], inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None, nsample_feature: int = 1000, nsample_outcome: int = 1000, threshold: float = 0.1, verbose: bool = False, seed: Optional[int] = None, device: Optional[torch.device] = None, dtype: Optional[torch.dtype] = None, ) -> Tuple[float, float]: r""" Monte Carlo estimate of the feasible volume with respect to feature constraints and outcome constraints. Args: bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`. model: The model used for sampling the outcomes. outcome_constraints: A list of callables, each mapping a Tensor of dimension `sample_shape x batch-shape x q x m` to a Tensor of dimension `sample_shape x batch-shape x q`, where negative values imply feasibility. inequality constraints: A list of tuples (indices, coefficients, rhs), with each tuple encoding an inequality constraint of the form `\sum_i (X[indices[i]] * coefficients[i]) >= rhs`. nsample_feature: The number of feature samples satisfying the bounds. nsample_outcome: The number of outcome samples from the model posterior. threshold: A lower limit for the probability of outcome feasibility seed: The seed for both feature and outcome samplers. If omitted, use a random seed. verbose: An indicator for whether to log the results. Returns: 2-element tuple containing: - Estimated proportion of volume in feature space that is feasible wrt the bounds and the inequality constraints (linear). - Estimated proportion of feasible features for which posterior samples (outcome) satisfies the outcome constraints with probability above the given threshold. """ seed = seed if seed is not None else torch.randint(0, 1000000, (1,)).item() with manual_seed(seed=seed): box_samples = bounds[0] + (bounds[1] - bounds[0]) * torch.rand( (nsample_feature, bounds.size(1)), dtype=dtype, device=device ) features, p_feature = get_feasible_samples( samples=box_samples, inequality_constraints=inequality_constraints ) # each new feature sample is a row p_outcome = get_outcome_feasibility_probability( model=model, X=features.unsqueeze(-2), outcome_constraints=outcome_constraints, threshold=threshold, nsample_outcome=nsample_outcome, seed=seed, ) if verbose: # pragma: no cover logger.info( "Proportion of volume that satisfies linear constraints: " + f"{p_feature:.4e}" ) if p_feature <= 0.01: logger.warning( "The proportion of satisfying volume is very low and may lead to " + "very long run times. Consider making your constraints less " + "restrictive." ) logger.info( "Proportion of linear-feasible volume that also satisfies each " + f"outcome constraint with probability > 0.1: {p_outcome:.4e}" ) if p_outcome <= 0.001: logger.warning( "The proportion of volume that also satisfies the outcome constraint " + "is very low. Consider making your parameter and outcome constraints " + "less restrictive." ) return p_feature, p_outcome