Source code for botorch.acquisition.knowledge_gradient

#!/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"""
Batch Knowledge Gradient (KG) via one-shot optimization as introduced in
[Balandat2020botorch]_. For broader discussion of KG see also [Frazier2008knowledge]_
and [Wu2016parallelkg]_.

.. [Balandat2020botorch]
    M. Balandat, B. Karrer, D. R. Jiang, S. Daulton, B. Letham, A. G. Wilson, and
    E. Bakshy. BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization.
    Advances in Neural Information Processing Systems 33, 2020.

.. [Frazier2008knowledge]
    P. Frazier, W. Powell, and S. Dayanik. A Knowledge-Gradient policy for
    sequential information collection. SIAM Journal on Control and Optimization,
    2008.

.. [Wu2016parallelkg]
    J. Wu and P. Frazier. The parallel knowledge gradient method for batch
    bayesian optimization. NIPS 2016.
"""

from __future__ import annotations

from copy import deepcopy
from typing import Any, Callable, Optional, Tuple, Union

import torch
from botorch import settings
from botorch.acquisition.acquisition import (
    AcquisitionFunction,
    OneShotAcquisitionFunction,
)
from botorch.acquisition.analytic import PosteriorMean
from botorch.acquisition.cost_aware import CostAwareUtility
from botorch.acquisition.monte_carlo import MCAcquisitionFunction, qSimpleRegret
from botorch.acquisition.objective import (
    AcquisitionObjective,
    MCAcquisitionObjective,
    ScalarizedObjective,
)
from botorch.exceptions.errors import UnsupportedError
from botorch.models.model import Model
from botorch.sampling.samplers import MCSampler, SobolQMCNormalSampler
from botorch.utils.transforms import (
    concatenate_pending_points,
    match_batch_shape,
    t_batch_mode_transform,
)
from torch import Tensor


[docs]class qKnowledgeGradient(MCAcquisitionFunction, OneShotAcquisitionFunction): r"""Batch Knowledge Gradient using one-shot optimization. This computes the batch Knowledge Gradient using fantasies for the outer expectation and either the model posterior mean or MC-sampling for the inner expectation. In addition to the design variables, the input `X` also includes variables for the optimal designs for each of the fantasy models. For a fixed number of fantasies, all parts of `X` can be optimized in a "one-shot" fashion. """ def __init__( self, model: Model, num_fantasies: Optional[int] = 64, sampler: Optional[MCSampler] = None, objective: Optional[AcquisitionObjective] = None, inner_sampler: Optional[MCSampler] = None, X_pending: Optional[Tensor] = None, current_value: Optional[Tensor] = None, **kwargs: Any, ) -> None: r"""q-Knowledge Gradient (one-shot optimization). Args: model: A fitted model. Must support fantasizing. num_fantasies: The number of fantasy points to use. More fantasy points result in a better approximation, at the expense of memory and wall time. Unused if `sampler` is specified. sampler: The sampler used to sample fantasy observations. Optional if `num_fantasies` is specified. objective: The objective under which the samples are evaluated. If `None` or a ScalarizedObjective, then the analytic posterior mean is used, otherwise the objective is MC-evaluated (using inner_sampler). inner_sampler: The sampler used for inner sampling. Ignored if the objective is `None` or a ScalarizedObjective. X_pending: A `m x d`-dim Tensor of `m` design points that have points that have been submitted for function evaluation but have not yet been evaluated. current_value: The current value, i.e. the expected best objective given the observed points `D`. If omitted, forward will not return the actual KG value, but the expected best objective given the data set `D u X`. """ if sampler is None: if num_fantasies is None: raise ValueError( "Must specify `num_fantasies` if no `sampler` is provided." ) # base samples should be fixed for joint optimization over X, X_fantasies sampler = SobolQMCNormalSampler( num_samples=num_fantasies, resample=False, collapse_batch_dims=True ) elif num_fantasies is not None: if sampler.sample_shape != torch.Size([num_fantasies]): raise ValueError( f"The sampler shape must match num_fantasies={num_fantasies}." ) else: num_fantasies = sampler.sample_shape[0] super(MCAcquisitionFunction, self).__init__(model=model) # if not explicitly specified, we use the posterior mean for linear objs if isinstance(objective, MCAcquisitionObjective) and inner_sampler is None: inner_sampler = SobolQMCNormalSampler( num_samples=128, resample=False, collapse_batch_dims=True ) if objective is None and model.num_outputs != 1: raise UnsupportedError( "Must specify an objective when using a multi-output model." ) self.sampler = sampler self.objective = objective self.set_X_pending(X_pending) self.inner_sampler = inner_sampler self.num_fantasies = num_fantasies self.current_value = current_value
[docs] @t_batch_mode_transform() def forward(self, X: Tensor) -> Tensor: r"""Evaluate qKnowledgeGradient on the candidate set `X`. Args: X: A `b x (q + num_fantasies) x d` Tensor with `b` t-batches of `q + num_fantasies` design points each. We split this X tensor into two parts in the `q` dimension (`dim=-2`). The first `q` are the q-batch of design points and the last num_fantasies are the current solutions of the inner optimization problem. `X_fantasies = X[..., -num_fantasies:, :]` `X_fantasies.shape = b x num_fantasies x d` `X_actual = X[..., :-num_fantasies, :]` `X_actual.shape = b x q x d` Returns: A Tensor of shape `b`. For t-batch b, the q-KG value of the design `X_actual[b]` is averaged across the fantasy models, where `X_fantasies[b, i]` is chosen as the final selection for the `i`-th fantasy model. NOTE: If `current_value` is not provided, then this is not the true KG value of `X_actual[b]`, and `X_fantasies[b, : ]` must be maximized at fixed `X_actual[b]`. """ X_actual, X_fantasies = _split_fantasy_points(X=X, n_f=self.num_fantasies) # We only concatenate X_pending into the X part after splitting if self.X_pending is not None: X_actual = torch.cat( [X_actual, match_batch_shape(self.X_pending, X_actual)], dim=-2 ) # construct the fantasy model of shape `num_fantasies x b` fantasy_model = self.model.fantasize( X=X_actual, sampler=self.sampler, observation_noise=True ) # get the value function value_function = _get_value_function( model=fantasy_model, objective=self.objective, sampler=self.inner_sampler ) # make sure to propagate gradients to the fantasy model train inputs with settings.propagate_grads(True): values = value_function(X=X_fantasies) # num_fantasies x b if self.current_value is not None: values = values - self.current_value # return average over the fantasy samples return values.mean(dim=0)
[docs] @concatenate_pending_points @t_batch_mode_transform() def evaluate(self, X_actual: Tensor, bounds: Tensor, **kwargs: Any) -> Tensor: r"""Evaluate qKnowledgeGradient on the candidate set `X_actual` by solving the inner optimization problem. Args: X_actual: A `b x q x d` Tensor with `b` t-batches of `q` design points each. Unlike `forward()`, this does not include solutions of the inner optimization problem. bounds: A `2 x d` tensor of lower and upper bounds for each column of the solutions to the inner problem. kwargs: Additional keyword arguments. This includes the options for optimization of the inner problem, i.e. `num_restarts`, `raw_samples`, an `options` dictionary to be passed on to the optimization helpers, and a `scipy_options` dictionary to be passed to `scipy.minimize`. Returns: A Tensor of shape `b`. For t-batch b, the q-KG value of the design `X_actual[b]` is averaged across the fantasy models. NOTE: If `current_value` is not provided, then this is not the true KG value of `X_actual[b]`. """ # construct the fantasy model of shape `num_fantasies x b` fantasy_model = self.model.fantasize( X=X_actual, sampler=self.sampler, observation_noise=True ) # get the value function value_function = _get_value_function( model=fantasy_model, objective=self.objective, sampler=self.inner_sampler ) # optimize the inner problem from botorch.optim.initializers import gen_value_function_initial_conditions from botorch.generation.gen import gen_candidates_scipy initial_conditions = gen_value_function_initial_conditions( acq_function=value_function, bounds=bounds, num_restarts=kwargs.get("num_restarts", 20), raw_samples=kwargs.get("raw_samples", 1024), current_model=self.model, options={**kwargs.get("options", {}), **kwargs.get("scipy_options", {})}, ) _, values = gen_candidates_scipy( initial_conditions=initial_conditions, acquisition_function=value_function, lower_bounds=bounds[0], upper_bounds=bounds[1], options=kwargs.get("scipy_options"), ) # get the maximizer for each batch values, _ = torch.max(values, dim=0) if self.current_value is not None: values = values - self.current_value # return average over the fantasy samples return values.mean(dim=0)
[docs] def get_augmented_q_batch_size(self, q: int) -> int: r"""Get augmented q batch size for one-shot optimization. Args: q: The number of candidates to consider jointly. Returns: The augmented size for one-shot optimization (including variables parameterizing the fantasy solutions). """ return q + self.num_fantasies
[docs] def extract_candidates(self, X_full: Tensor) -> Tensor: r"""We only return X as the set of candidates post-optimization. Args: X_full: A `b x (q + num_fantasies) x d`-dim Tensor with `b` t-batches of `q + num_fantasies` design points each. Returns: A `b x q x d`-dim Tensor with `b` t-batches of `q` design points each. """ return X_full[..., : -self.num_fantasies, :]
[docs]class qMultiFidelityKnowledgeGradient(qKnowledgeGradient): r"""Batch Knowledge Gradient for multi-fidelity optimization. A version of `qKnowledgeGradient` that supports multi-fidelity optimization via a `CostAwareUtility` and the `project` and `expand` operators. If none of these are set, this acquisition function reduces to `qKnowledgeGradient`. """ def __init__( self, model: Model, num_fantasies: Optional[int] = 64, sampler: Optional[MCSampler] = None, objective: Optional[AcquisitionObjective] = None, inner_sampler: Optional[MCSampler] = None, X_pending: Optional[Tensor] = None, current_value: Optional[Tensor] = None, cost_aware_utility: Optional[CostAwareUtility] = None, project: Callable[[Tensor], Tensor] = lambda X: X, expand: Callable[[Tensor], Tensor] = lambda X: X, **kwargs: Any, ) -> None: r"""Multi-Fidelity q-Knowledge Gradient (one-shot optimization). Args: model: A fitted model. Must support fantasizing. num_fantasies: The number of fantasy points to use. More fantasy points result in a better approximation, at the expense of memory and wall time. Unused if `sampler` is specified. sampler: The sampler used to sample fantasy observations. Optional if `num_fantasies` is specified. objective: The objective under which the samples are evaluated. If `None` or a ScalarizedObjective, then the analytic posterior mean is used, otherwise the objective is MC-evaluated (using inner_sampler). inner_sampler: The sampler used for inner sampling. Ignored if the objective is `None` or a ScalarizedObjective. X_pending: A `m x d`-dim Tensor of `m` design points that have points that have been submitted for function evaluation but have not yet been evaluated. current_value: The current value, i.e. the expected best objective given the observed points `D`. If omitted, forward will not return the actual KG value, but the expected best objective given the data set `D u X`. cost_aware_utility: A CostAwareUtility computing the cost-transformed utility from a candidate set and samples of increases in utility. project: A callable mapping a `batch_shape x q x d` tensor of design points to a tensor of the same shape projected to the desired target set (e.g. the target fidelities in case of multi-fidelity optimization). expand: A callable mapping a `batch_shape x q x d` input tensor to a `batch_shape x (q + q_e)' x d`-dim output tensor, where the `q_e` additional points in each q-batch correspond to additional ("trace") observations. """ if current_value is None and cost_aware_utility is not None: raise UnsupportedError( "Cost-aware KG requires current_value to be specified." ) super().__init__( model=model, num_fantasies=num_fantasies, sampler=sampler, objective=objective, inner_sampler=inner_sampler, X_pending=X_pending, current_value=current_value, ) self.cost_aware_utility = cost_aware_utility self.project = project self.expand = expand self._cost_sampler = None @property def cost_sampler(self): if self._cost_sampler is None: # Note: Using the deepcopy here is essential. Removing this poses a # problem if the base model and the cost model have a different number # of outputs or test points (this would be caused by expand), as this # would trigger re-sampling the base samples in the fantasy sampler. # By cloning the sampler here, the right thing will happen if the # the sizes are compatible, if they are not this will result in # samples being drawn using different base samples, but it will at # least avoid changing state of the fantasy sampler. self._cost_sampler = deepcopy(self.sampler) return self._cost_sampler
[docs] @t_batch_mode_transform() def forward(self, X: Tensor) -> Tensor: r"""Evaluate qMultiFidelityKnowledgeGradient on the candidate set `X`. Args: X: A `b x (q + num_fantasies) x d` Tensor with `b` t-batches of `q + num_fantasies` design points each. We split this X tensor into two parts in the `q` dimension (`dim=-2`). The first `q` are the q-batch of design points and the last num_fantasies are the current solutions of the inner optimization problem. `X_fantasies = X[..., -num_fantasies:, :]` `X_fantasies.shape = b x num_fantasies x d` `X_actual = X[..., :-num_fantasies, :]` `X_actual.shape = b x q x d` In addition, `X` may be augmented with fidelity parameteres as part of thee `d`-dimension. Projecting fidelities to the target fidelity is handled by `project`. Returns: A Tensor of shape `b`. For t-batch b, the q-KG value of the design `X_actual[b]` is averaged across the fantasy models, where `X_fantasies[b, i]` is chosen as the final selection for the `i`-th fantasy model. NOTE: If `current_value` is not provided, then this is not the true KG value of `X_actual[b]`, and `X_fantasies[b, : ]` must be maximized at fixed `X_actual[b]`. """ X_actual, X_fantasies = _split_fantasy_points(X=X, n_f=self.num_fantasies) # We only concatenate X_pending into the X part after splitting if self.X_pending is not None: X_eval = torch.cat( [X_actual, match_batch_shape(self.X_pending, X_actual)], dim=-2 ) else: X_eval = X_actual # construct the fantasy model of shape `num_fantasies x b` # expand X (to potentially add trace observations) fantasy_model = self.model.fantasize( X=self.expand(X_eval), sampler=self.sampler, observation_noise=True ) # get the value function value_function = _get_value_function( model=fantasy_model, objective=self.objective, sampler=self.inner_sampler ) # make sure to propagate gradients to the fantasy model train inputs # project the fantasy points with settings.propagate_grads(True): values = value_function(X=self.project(X_fantasies)) # num_fantasies x b if self.current_value is not None: values = values - self.current_value if self.cost_aware_utility is not None: values = self.cost_aware_utility( X=X_actual, deltas=values, sampler=self.cost_sampler ) # return average over the fantasy samples return values.mean(dim=0)
def _get_value_function( model: Model, objective: Optional[Union[MCAcquisitionObjective, ScalarizedObjective]] = None, sampler: Optional[MCSampler] = None, ) -> AcquisitionFunction: r"""Construct value function (i.e. inner acquisition function).""" if isinstance(objective, MCAcquisitionObjective): return qSimpleRegret(model=model, sampler=sampler, objective=objective) else: return PosteriorMean(model=model, objective=objective) def _split_fantasy_points(X: Tensor, n_f: int) -> Tuple[Tensor, Tensor]: r"""Split a one-shot optimization input into actual and fantasy points Args: X: A `batch_shape x (q + n_f) x d`-dim tensor of actual and fantasy points Returns: 2-element tuple containing - A `batch_shape x q x d`-dim tensor `X_actual` of input candidates. - A `n_f x batch_shape x 1 x d`-dim tensor `X_fantasies` of fantasy points, where `X_fantasies[i, batch_idx]` is the i-th fantasy point associated with the batch indexed by `batch_idx`. """ if n_f > X.size(-2): raise ValueError( f"n_f ({n_f}) must be less than the q-batch dimension of X ({X.size(-2)})" ) split_sizes = [X.size(-2) - n_f, n_f] X_actual, X_fantasies = torch.split(X, split_sizes, dim=-2) # X_fantasies is b x num_fantasies x d, needs to be num_fantasies x b x 1 x d # for batch mode evaluation with batch shape num_fantasies x b. # b x num_fantasies x d --> num_fantasies x b x d X_fantasies = X_fantasies.permute(-2, *range(X_fantasies.dim() - 2), -1) # num_fantasies x b x 1 x d X_fantasies = X_fantasies.unsqueeze(dim=-2) return X_actual, X_fantasies