#!/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.
r"""
Objective Modules to be used with acquisition functions.
"""
from __future__ import annotations
from abc import ABC, abstractmethod
from typing import Callable, List
import torch
from botorch.posteriors.gpytorch import GPyTorchPosterior, scalarize_posterior
from botorch.utils import apply_constraints
from torch import Tensor
from torch.nn import Module
[docs]class AcquisitionObjective(Module, ABC):
r"""Abstract base class for objectives."""
...
[docs]class ScalarizedObjective(AcquisitionObjective):
r"""Affine objective to be used with analytic acquisition functions.
For a Gaussian posterior at a single point (`q=1`) with mean `mu` and
covariance matrix `Sigma`, this yields a single-output posterior with mean
`weights^T * mu` and variance `weights^T Sigma w`.
Example:
Example for a model with two outcomes:
>>> weights = torch.tensor([0.5, 0.25])
>>> objective = ScalarizedObjective(weights)
>>> EI = ExpectedImprovement(model, best_f=0.1, objective=objective)
"""
def __init__(self, weights: Tensor, offset: float = 0.0) -> None:
r"""Affine objective.
Args:
weights: A one-dimensional tensor with `m` elements representing the
linear weights on the outputs.
offset: An offset to be added to posterior mean.
"""
if weights.dim() != 1:
raise ValueError("weights must be a one-dimensional tensor.")
super().__init__()
self.register_buffer("weights", weights)
self.offset = offset
[docs] def forward(self, posterior: GPyTorchPosterior) -> GPyTorchPosterior:
r"""Compute the posterior of the affine transformation.
Args:
posterior: A posterior with the same number of outputs as the
elements in `self.weights`.
Returns:
A single-output posterior.
"""
return scalarize_posterior(
posterior=posterior, weights=self.weights, offset=self.offset
)
[docs]class MCAcquisitionObjective(AcquisitionObjective):
r"""Abstract base class for MC-based objectives."""
[docs] @abstractmethod
def forward(self, samples: Tensor) -> Tensor:
r"""Evaluate the objective on the samples.
Args:
samples: A `sample_shape x batch_shape x q x m`-dim Tensors of
samples from a model posterior.
Returns:
Tensor: A `sample_shape x batch_shape x q`-dim Tensor of objective
values (assuming maximization).
This method is usually not called directly, but via the objectives
Example:
>>> # `__call__` method:
>>> samples = sampler(posterior)
>>> outcome = mc_obj(samples)
"""
pass # pragma: no cover
[docs]class IdentityMCObjective(MCAcquisitionObjective):
r"""Trivial objective extracting the last dimension.
Example:
>>> identity_objective = IdentityMCObjective()
>>> samples = sampler(posterior)
>>> objective = identity_objective(samples)
"""
[docs] def forward(self, samples: Tensor) -> Tensor:
return samples.squeeze(-1)
[docs]class LinearMCObjective(MCAcquisitionObjective):
r"""Linear objective constructed from a weight tensor.
For input `samples` and `mc_obj = LinearMCObjective(weights)`, this produces
`mc_obj(samples) = sum_{i} weights[i] * samples[..., i]`
Example:
Example for a model with two outcomes:
>>> weights = torch.tensor([0.75, 0.25])
>>> linear_objective = LinearMCObjective(weights)
>>> samples = sampler(posterior)
>>> objective = linear_objective(samples)
"""
def __init__(self, weights: Tensor) -> None:
r"""Linear Objective.
Args:
weights: A one-dimensional tensor with `m` elements representing the
linear weights on the outputs.
"""
super().__init__()
if weights.dim() != 1:
raise ValueError("weights must be a one-dimensional tensor.")
self.register_buffer("weights", weights)
[docs] def forward(self, samples: Tensor) -> Tensor:
r"""Evaluate the linear objective on the samples.
Args:
samples: A `sample_shape x batch_shape x q x m`-dim tensors of
samples from a model posterior.
Returns:
A `sample_shape x batch_shape x q`-dim tensor of objective values.
"""
if samples.shape[-1] != self.weights.shape[-1]:
raise RuntimeError("Output shape of samples not equal to that of weights")
return torch.einsum("...m, m", [samples, self.weights])
[docs]class GenericMCObjective(MCAcquisitionObjective):
r"""Objective generated from a generic callable.
Allows to construct arbitrary MC-objective functions from a generic
callable. In order to be able to use gradient-based acquisition function
optimization it should be possible to backpropagate through the callable.
Example:
>>> generic_objective = GenericMCObjective(lambda Y: torch.sqrt(Y).sum(dim=-1))
>>> samples = sampler(posterior)
>>> objective = generic_objective(samples)
"""
def __init__(self, objective: Callable[[Tensor], Tensor]) -> None:
r"""Objective generated from a generic callable.
Args:
objective: A callable mapping a `sample_shape x batch-shape x q x m`-
dim Tensor to a `sample_shape x batch-shape x q`-dim Tensor of
objective values.
"""
super().__init__()
self.objective = objective
[docs] def forward(self, samples: Tensor) -> Tensor:
r"""Evaluate the feasibility-weigthed objective on the samples.
Args:
samples: A `sample_shape x batch_shape x q x m`-dim Tensors of
samples from a model posterior.
Returns:
A `sample_shape x batch_shape x q`-dim Tensor of objective values
weighted by feasibility (assuming maximization).
"""
return self.objective(samples)
[docs]class ConstrainedMCObjective(GenericMCObjective):
r"""Feasibility-weighted objective.
An Objective allowing to maximize some scalable objective on the model
outputs subject to a number of constraints. Constraint feasibilty is
approximated by a sigmoid function.
`mc_acq(X) = objective(X) * prod_i (1 - sigmoid(constraint_i(X)))`
TODO: Document functional form exactly.
See `botorch.utils.objective.apply_constraints` for details on the constarint
handling.
Example:
>>> bound = 0.0
>>> objective = lambda Y: Y[..., 0]
>>> # apply non-negativity constraint on f(x)[1]
>>> constraint = lambda Y: bound - Y[..., 1]
>>> constrained_objective = ConstrainedMCObjective(objective, [constraint])
>>> samples = sampler(posterior)
>>> objective = constrained_objective(samples)
"""
def __init__(
self,
objective: Callable[[Tensor], Tensor],
constraints: List[Callable[[Tensor], Tensor]],
infeasible_cost: float = 0.0,
eta: float = 1e-3,
) -> None:
r"""Feasibility-weighted objective.
Args:
objective: A callable mapping a `sample_shape x batch-shape x q x m`-
dim Tensor to a `sample_shape x batch-shape x q`-dim Tensor of
objective values.
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.
infeasible_cost: The cost of a design if all associated samples are
infeasible.
eta: The temperature parameter of the sigmoid function approximating
the constraint.
"""
super().__init__(objective=objective)
self.constraints = constraints
self.eta = eta
self.register_buffer("infeasible_cost", torch.tensor(infeasible_cost))
[docs] def forward(self, samples: Tensor) -> Tensor:
r"""Evaluate the feasibility-weighted objective on the samples.
Args:
samples: A `sample_shape x batch_shape x q x m`-dim Tensors of
samples from a model posterior.
Returns:
A `sample_shape x batch_shape x q`-dim Tensor of objective values
weighted by feasibility (assuming maximization).
"""
obj = super().forward(samples=samples)
return apply_constraints(
obj=obj,
constraints=self.constraints,
samples=samples,
infeasible_cost=self.infeasible_cost,
eta=self.eta,
)
