Source code for botorch.utils.objective

#!/usr/bin/env python3

# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved

r"""
Helpers for handling objectives.
"""

from typing import Callable, List, Optional

import torch
from torch import Tensor


[docs]def get_objective_weights_transform( weights: Optional[Tensor] ) -> Callable[[Tensor], Tensor]: r"""Create a linear objective callable from a set of weights. Create a callable mapping a Tensor of size `b x q x m` to a Tensor of size `b x q`, where `m` is the number of outputs of the model using scalarization via the objective weights. This callable supports broadcasting (e.g. for calling on a tensor of shape `mc_samples x b x q x m`). For `m = 1`, the objective weight is used to determine the optimization direction. Args: weights: a 1-dimensional Tensor containing a weight for each task. If not provided, the identity mapping is used. Returns: Transform function using the objective weights. Example: >>> weights = torch.tensor([0.75, 0.25]) >>> transform = get_objective_weights_transform(weights) """ # if no weights provided, just extract the single output if weights is None: return lambda Y: Y.squeeze(-1) def _objective(Y): r"""Evaluate objective. Note: einsum multiples Y by weights and sums over the `m`-dimension. Einsum is ~2x faster than using `(Y * weights.view(1, 1, -1)).sum(dim-1)`. Args: Y: A `... x b x q x m` tensor of function values. Returns: A `... x b x q`-dim tensor of objective values. """ return torch.einsum("...m, m", [Y, weights]) return _objective
[docs]def apply_constraints_nonnegative_soft( obj: Tensor, constraints: List[Callable[[Tensor], Tensor]], samples: Tensor, eta: float, ) -> Tensor: r"""Applies constraints to a non-negative objective. This function uses a sigmoid approximation to an indicator function for each constraint. Args: obj: A `n_samples x b x q` Tensor of objective values. constraints: A list of callables, each mapping a Tensor of size `b x q x m` to a Tensor of size `b x q`, where negative values imply feasibility. This callable must support broadcasting. Only relevant for multi- output models (`m` > 1). samples: A `b x q x m` Tensor of samples drawn from the posterior. eta: The temperature parameter for the sigmoid function. Returns: A `n_samples x b x q`-dim tensor of feasibility-weighted objectives. """ obj = obj.clamp_min(0) # Enforce non-negativity with constraints for constraint in constraints: obj = obj.mul(soft_eval_constraint(constraint(samples), eta=eta)) return obj
[docs]def soft_eval_constraint(lhs: Tensor, eta: float = 1e-3) -> Tensor: r"""Element-wise evaluation of a constraint in a 'soft' fashion `value(x) = 1 / (1 + exp(x / eta))` Args: lhs: The left hand side of the constraint `lhs <= 0`. eta: The temperature parameter of the softmax function. As eta grows larger, this approximates the Heaviside step function. Returns: Element-wise 'soft' feasibility indicator of the same shape as `lhs`. For each element `x`, `value(x) -> 0` as `x` becomes positive, and `value(x) -> 1` as x becomes negative. """ if eta <= 0: raise ValueError("eta must be positive") return torch.sigmoid(-lhs / eta)
[docs]def apply_constraints( obj: Tensor, constraints: List[Callable[[Tensor], Tensor]], samples: Tensor, infeasible_cost: float, eta: float = 1e-3, ) -> Tensor: r"""Apply constraints using an infeasible_cost `M` for negative objectives. This allows feasibility-weighting an objective for the case where the objective can be negative by usingthe following strategy: (1) add `M` to make obj nonnegative (2) apply constraints using the sigmoid approximation (3) shift by `-M` Args: obj: A `n_samples x b x q` Tensor of objective values. constraints: A list of callables, each mapping a Tensor of size `b x q x m` to a Tensor of size `b x q`, where negative values imply feasibility. This callable must support broadcasting. Only relevant for multi- output models (`m` > 1). samples: A `b x q x m` Tensor of samples drawn from the posterior. infeasible_cost: The infeasible value. eta: The temperature parameter of the sigmoid function. Returns: A `n_samples x b x q`-dim tensor of feasibility-weighted objectives. """ # obj has dimensions n_samples x b x q obj = obj.add(infeasible_cost) # now it is nonnegative obj = apply_constraints_nonnegative_soft( obj=obj, constraints=constraints, samples=samples, eta=eta ) return obj.add(-infeasible_cost)