#!/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"""
Sampling-based generation strategies.
A SamplingStrategy returns samples from the input points (i.e. Tensors in feature
space), rather than the value for a set of tensors, as acquisition functions do.
The q-batch dimension has similar semantics as for acquisition functions in that the
points across the q-batch are considered jointly for sampling (where as for
q-acquisition functions we evaluate the joint value of the q-batch).
"""
from __future__ import annotations
from abc import ABC, abstractmethod
from typing import Any, Optional
import torch
from torch import Tensor
from torch.nn import Module
from ..acquisition.acquisition import AcquisitionFunction
from ..acquisition.objective import (
AcquisitionObjective,
IdentityMCObjective,
ScalarizedObjective,
)
from ..models.model import Model
from ..sampling.samplers import IIDNormalSampler
from ..utils.sampling import batched_multinomial
from ..utils.transforms import standardize
from .utils import _flip_sub_unique
[docs]class SamplingStrategy(Module, ABC):
r"""Abstract base class for sampling-based generation strategies."""
[docs] @abstractmethod
def forward(self, X: Tensor, num_samples: int = 1, **kwargs: Any) -> Tensor:
r"""Sample according to the SamplingStrategy.
Args:
X: A `batch_shape x N x d`-dim Tensor from which to sample (in the `N`
dimension).
num_samples: The number of samples to draw.
kwargs: Additional implementation-specific kwargs.
Returns:
A `batch_shape x num_samples x d`-dim Tensor of samples from `X`, where
`X[..., i, :]` is the `i`-th sample.
"""
pass # pragma: no cover
[docs]class MaxPosteriorSampling(SamplingStrategy):
r"""Sample from a set of points according to their max posterior value.
Example:
>>> MPS = MaxPosteriorSampling(model) # model w/ feature dim d=3
>>> X = torch.rand(2, 100, 3)
>>> sampled_X = MPS(X, n=5)
"""
def __init__(
self,
model: Model,
objective: Optional[AcquisitionObjective] = None,
replacement: bool = True,
) -> None:
r"""Constructor for the SamplingStrategy base class.
Args:
model: A fitted model.
objective: The objective. Typically, the AcquisitionObjective under which
the samples are evaluated. If a ScalarizedObjective, samples from the
scalarized posterior are used. Defaults to `IdentityMCObjective()`.
replacement: If True, sample with replacement.
"""
super().__init__()
self.model = model
if objective is None:
objective = IdentityMCObjective()
self.objective = objective
self.replacement = replacement
[docs] def forward(
self, X: Tensor, num_samples: int = 1, observation_noise: bool = False
) -> Tensor:
r"""Sample from the model posterior.
Args:
X: A `batch_shape x N x d`-dim Tensor from which to sample (in the `N`
dimension) according to the maximum posterior value under the objective.
num_samples: The number of samples to draw.
observation_noise: If True, sample with observation noise.
Returns:
A `batch_shape x num_samples x d`-dim Tensor of samples from `X`, where
`X[..., i, :]` is the `i`-th sample.
"""
posterior = self.model.posterior(X, observation_noise=observation_noise)
if isinstance(self.objective, ScalarizedObjective):
posterior = self.objective(posterior)
sampler = IIDNormalSampler(
num_samples=num_samples, collapse_batch_dims=False, resample=True
)
samples = sampler(posterior) # num_samples x batch_shape x N x m
if isinstance(self.objective, ScalarizedObjective):
obj = samples.squeeze(-1) # num_samples x batch_shape x N
else:
obj = self.objective(samples) # num_samples x batch_shape x N
if self.replacement:
# if we allow replacement then things are simple(r)
idcs = torch.argmax(obj, dim=-1)
else:
# if we need to deduplicate we have to do some tensor acrobatics
# first we get the indices associated w/ the num_samples top samples
_, idcs_full = torch.topk(obj, num_samples, dim=-1)
# generate some indices to smartly index into the lower triangle of
# idcs_full (broadcasting across batch dimensions)
ridx, cindx = torch.tril_indices(num_samples, num_samples)
# pick the unique indices in order - since we look at the lower triangle
# of the index matrix and we don't sort, this achieves deduplication
sub_idcs = idcs_full[ridx, ..., cindx]
if sub_idcs.ndim == 1:
idcs = _flip_sub_unique(sub_idcs, num_samples)
elif sub_idcs.ndim == 2:
# TODO: Find a better way to do this
n_b = sub_idcs.size(-1)
idcs = torch.stack(
[_flip_sub_unique(sub_idcs[:, i], num_samples) for i in range(n_b)],
dim=-1,
)
else:
# TODO: Find a general way to do this efficiently.
raise NotImplementedError(
"MaxPosteriorSampling without replacement for more than a single "
"batch dimension is not yet implemented."
)
# idcs is num_samples x batch_shape, to index into X we need to permute for it
# to have shape batch_shape x num_samples
if idcs.ndim > 1:
idcs = idcs.permute(*range(1, idcs.ndim), 0)
# in order to use gather, we need to repeat the index tensor d times
idcs = idcs.unsqueeze(-1).expand(*idcs.shape, X.size(-1))
# now if the model is batched batch_shape will not necessarily be the
# batch_shape of X, so we expand X to the proper shape
Xe = X.expand(*obj.shape[1:], X.size(-1))
# finally we can gather along the N dimension
return torch.gather(Xe, -2, idcs)
[docs]class BoltzmannSampling(SamplingStrategy):
r"""Sample from a set of points according to a tempered acquisition value.
Given an acquisition function `acq_func`, this sampling strategies draws
samples from a `batch_shape x N x d`-dim tensor `X` according to a multinomial
distribution over its indices given by
weight(X[..., i, :]) ~ exp(eta * standardize(acq_func(X[..., i, :])))
where `standardize(Y)` standardizes `Y` to zero mean and unit variance. As the
temperature parameter `eta -> 0`, this approaches uniform sampling, while as
`eta -> infty`, this approaches selecting the maximizer(s) of the acquisition
function `acq_func`.
Example:
>>> UCB = UpperConfidenceBound(model, beta=0.1)
>>> BMUCB = BoltzmannSampling(UCB, eta=0.5)
>>> X = torch.rand(2, 100, 3)
>>> sampled_X = BMUCB(X, n=5)
"""
def __init__(
self, acq_func: AcquisitionFunction, eta: float = 1.0, replacement: bool = True
) -> None:
r"""Boltzmann Acquisition Value Sampling.
Args:
acq_func: The acquisition function; to be evaluated in batch at the
individual points of a q-batch (not jointly, as is the case for
acquisition functions). Can be analytic or Monte-Carlo.
eta: The temperature parameter in the softmax.
replacement: If True, sample with replacement.
"""
super().__init__()
self.acq_func = acq_func
self.eta = eta
self.replacement = replacement
[docs] def forward(self, X: Tensor, num_samples: int = 1) -> Tensor:
r"""Sample from a tempered value of the acquisition function value.
Args:
X: A `batch_shape x N x d`-dim Tensor from which to sample (in the `N`
dimension) according to the maximum posterior value under the objective.
Note that if a batched model is used in the underlying acquisition
function, then its batch shape must be broadcastable to `batch_shape`.
num_samples: The number of samples to draw.
Returns:
A `batch_shape x num_samples x d`-dim Tensor of samples from `X`, where
`X[..., i, :]` is the `i`-th sample.
"""
# TODO: Can we get the model batch shape property from the model?
# we move the `N` dimension to the front for evaluating the acquisition function
# so that X_eval has shape `N x batch_shape x 1 x d`
X_eval = X.permute(-2, *range(X.ndim - 2), -1).unsqueeze(-2)
acqval = self.acq_func(X_eval) # N x batch_shape
# now move the `N` dimension back (this is the number of categories)
acqval = acqval.permute(*range(1, X.ndim - 1), 0) # batch_shape x N
weights = torch.exp(self.eta * standardize(acqval)) # batch_shape x N
idcs = batched_multinomial(
weights=weights, num_samples=num_samples, replacement=self.replacement
)
# now do some gathering acrobatics to select the right elements from X
return torch.gather(X, -2, idcs.unsqueeze(-1).expand(*idcs.shape, X.size(-1)))
