#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
r"""
Preference acquisition functions. This includes:
Analytical EUBO acquisition function as introduced in [Lin2022preference]_
and its MC-based generalization qEUBO as proposed in [Astudillo2023qeubo]_.
.. [Astudillo2023qeubo]
Astudillo, R., Lin, Z.J., Bakshy, E. and Frazier, P.I. qEUBO: A Decision-Theoretic
Acquisition Function for Preferential Bayesian Optimization. International
Conference on Artificial Intelligence and Statistics (AISTATS), 2023.
.. [Lin2022preference]
Lin, Z.J., Astudillo, R., Frazier, P.I. and Bakshy, E. Preference Exploration
for Efficient Bayesian Optimization with Multiple Outcomes. International
Conference on Artificial Intelligence and Statistics (AISTATS), 2022.
.. [Houlsby2011bald]
Houlsby, N., Huszár, F., Ghahramani, Z. and Lengyel, M.
Bayesian Active Learning for Gaussian Process Classification.
NIPS Workshop on Bayesian optimization, experimental design and bandits:
Theory and applications, 2011.
"""
from __future__ import annotations
from typing import Optional
import torch
from botorch.acquisition import AnalyticAcquisitionFunction
from botorch.acquisition.monte_carlo import MCAcquisitionFunction
from botorch.acquisition.objective import MCAcquisitionObjective, PosteriorTransform
from botorch.exceptions.errors import UnsupportedError
from botorch.models.deterministic import DeterministicModel
from botorch.models.model import Model
from botorch.sampling.base import MCSampler
from botorch.utils.transforms import (
concatenate_pending_points,
match_batch_shape,
t_batch_mode_transform,
)
from torch import Tensor
from torch.distributions import Bernoulli, Normal
SIGMA_JITTER = 1e-8
[docs]
class AnalyticExpectedUtilityOfBestOption(AnalyticAcquisitionFunction):
r"""Analytic Preferential Expected Utility of Best Options, i.e., Analytical EUBO"""
def __init__(
self,
pref_model: Model,
outcome_model: Optional[DeterministicModel] = None,
previous_winner: Optional[Tensor] = None,
) -> None:
r"""Analytic implementation of Expected Utility of the Best Option under the
Laplace model (assumes a PairwiseGP is used as the preference model) as
proposed in [Lin2022preference]_.
Args:
pref_model: The preference model that maps the outcomes (i.e., Y) to
scalar-valued utility.
outcome_model: A deterministic model that maps parameters (i.e., X) to
outcomes (i.e., Y). The outcome model f defines the search space of
Y = f(X). If model is None, we are directly calculating EUBO on
the parameter space. When used with `OneSamplePosteriorDrawModel`,
we are obtaining EUBO-zeta as described in [Lin2022preference]_.
previous_winner: Tensor representing the previous winner in the Y space.
"""
super().__init__(model=pref_model)
# ensure the model is in eval mode
self.add_module("outcome_model", outcome_model)
self.register_buffer("previous_winner", previous_winner)
tkwargs = {
"dtype": pref_model.datapoints.dtype,
"device": pref_model.datapoints.device,
}
std_norm = torch.distributions.normal.Normal(
torch.zeros(1, **tkwargs),
torch.ones(1, **tkwargs),
)
self.std_norm = std_norm
[docs]
@t_batch_mode_transform()
def forward(self, X: Tensor) -> Tensor:
r"""Evaluate analytical EUBO on the candidate set X.
Args:
X: A `batch_shape x q x d`-dim Tensor, where `q = 2` if `previous_winner`
is not `None`, and `q = 1` otherwise.
Returns:
The acquisition value for each batch as a tensor of shape `batch_shape`.
"""
if not (
((X.shape[-2] == 2) and (self.previous_winner is None))
or ((X.shape[-2] == 1) and (self.previous_winner is not None))
):
raise UnsupportedError(
f"{self.__class__.__name__} only support q=2 or q=1"
"with a previous winner specified"
)
Y = X if self.outcome_model is None else self.outcome_model(X)
if self.previous_winner is not None:
Y = torch.cat([Y, match_batch_shape(self.previous_winner, Y)], dim=-2)
pref_posterior = self.model.posterior(Y)
pref_mean = pref_posterior.mean.squeeze(-1)
pref_cov = pref_posterior.covariance_matrix
delta = pref_mean[..., 0] - pref_mean[..., 1]
w = torch.tensor([1.0, -1.0], dtype=pref_cov.dtype, device=pref_cov.device)
var = w @ pref_cov @ w
sigma = torch.sqrt(var.clamp(min=SIGMA_JITTER))
u = delta / sigma
ucdf = self.std_norm.cdf(u)
updf = torch.exp(self.std_norm.log_prob(u))
acqf_val = sigma * (updf + u * ucdf)
if self.previous_winner is None:
acqf_val = acqf_val + pref_mean[..., 1]
return acqf_val
[docs]
class qExpectedUtilityOfBestOption(MCAcquisitionFunction):
r"""MC-based Expected Utility of Best Option (qEUBO)
This computes qEUBO by
(1) sampling the joint posterior over q points
(2) evaluating the maximum objective value accross the q points
(3) averaging over the samples
`qEUBO(X) = E[max Y], Y ~ f(X), where X = (x_1,...,x_q)`
"""
def __init__(
self,
pref_model: Model,
outcome_model: Optional[DeterministicModel] = None,
sampler: Optional[MCSampler] = None,
objective: Optional[MCAcquisitionObjective] = None,
posterior_transform: Optional[PosteriorTransform] = None,
X_pending: Optional[Tensor] = None,
) -> None:
r"""MC-based Expected Utility of Best Option (qEUBO) as proposed
in [Astudillo2023qeubo]_.
Args:
pref_model: The preference model that maps the outcomes (i.e., Y) to
scalar-valued utility.
outcome_model: A deterministic model that maps parameters (i.e., X) to
outcomes (i.e., Y). The outcome model f defines the search space of
Y = f(X). If model is None, we are directly calculating qEUBO on
the parameter space.
sampler: The sampler used to draw base samples. See `MCAcquisitionFunction`
more details.
objective: The MCAcquisitionObjective under which the samples are evaluated.
Defaults to `IdentityMCObjective()`.
posterior_transform: A PosteriorTransform (optional).
X_pending: A `m x d`-dim Tensor of `m` design points that have been
submitted for function evaluation but have not yet been evaluated.
Concatenated into X upon forward call. Copied and set
to have no gradient.
"""
super().__init__(
model=pref_model,
sampler=sampler,
objective=objective,
posterior_transform=posterior_transform,
X_pending=X_pending,
)
# ensure the model is in eval mode
self.add_module("outcome_model", outcome_model)
[docs]
@concatenate_pending_points
@t_batch_mode_transform()
def forward(self, X: Tensor) -> Tensor:
r"""Evaluate qEUBO on the candidate set `X`.
Args:
X: A `batch_shape x q x d`-dim Tensor of t-batches with `q`
`d`-dim design points each.
Returns:
A `batch_shape'`-dim Tensor of qEUBO values at the given design
points `X`, where `batch_shape'` is the broadcasted batch shape
of model and input `X`.
"""
Y = X if self.outcome_model is None else self.outcome_model(X)
_, obj = self._get_samples_and_objectives(Y)
obj_best = obj.max(dim=-1).values
return obj_best.mean(dim=0)
[docs]
class PairwiseBayesianActiveLearningByDisagreement(MCAcquisitionFunction):
r"""MC Bayesian Active Learning by Disagreement"""
def __init__(
self,
pref_model: Model,
outcome_model: Optional[DeterministicModel] = None,
num_samples: Optional[int] = 1024,
std_noise: Optional[float] = 0.0,
) -> None:
"""
Monte Carlo implementation of Bayesian Active Learning by Disagreement (BALD)
proposed in [Houlsby2011bald]_.
Args:
pref_model: The preference model that maps the outcomes (i.e., Y) to
scalar-valued utility.
outcome_model: A deterministic model that maps parameters (i.e., X) to
outcomes (i.e., Y). The outcome model f defines the search space of
Y = f(X). If model is None, we are directly calculating BALD on
the parameter space.
num_samples: number of samples to approximate the conditional_entropy.
std_noise: Additional observational noise to include. Defaults to 0.
"""
super().__init__(model=pref_model)
# ensure the model is in eval mode
self.add_module("outcome_model", outcome_model)
self.num_samples = num_samples
# assuming the relative observation noise is fixed at 1.0 (e.g., in PairwiseGP)
self.std_noise = std_noise
self.std_normal = Normal(0, 1)
[docs]
@t_batch_mode_transform(expected_q=2)
def forward(self, X: Tensor) -> Tensor:
r"""Evaluate MC BALD on the candidate set `X`.
Args:
X: A `batch_shape x 2 x d`-dim Tensor of t-batches with `q=2`
`d`-dim design points each.
Returns:
A `batch_shape'`-dim Tensor of MC BALD values at the given
design points pair `X`, where `batch_shape'` is the broadcasted
batch shape of model and input `X`.
"""
Y = X if self.outcome_model is None else self.outcome_model(X)
pref_posterior = self.model.posterior(Y)
pref_mean = pref_posterior.mean.squeeze(-1)
pref_cov = pref_posterior.covariance_matrix
mu = pref_mean[..., 0] - pref_mean[..., 1]
w = torch.tensor([1.0, -1.0], dtype=pref_cov.dtype, device=pref_cov.device)
var = 2 * self.std_noise + w @ pref_cov @ w
sigma = torch.sqrt(var.clamp(min=SIGMA_JITTER))
# eq (3) in Houlsby, et al. (2011)
posterior_entropies = Bernoulli(
self.std_normal.cdf(mu / torch.sqrt(var + 1))
).entropy()
# Sample-based approx to eq (4) in Houlsby, et al. (2011)
obj_samples = self.std_normal.cdf(
Normal(loc=mu, scale=sigma).rsample(torch.Size([self.num_samples]))
)
sample_entropies = Bernoulli(obj_samples).entropy()
conditional_entropies = sample_entropies.mean(dim=0)
return posterior_entropies - conditional_entropies
