Add entropy search acquisition functions (#1458)

Summary:
Hi,

I have provided some implementations of entropy search acquisition functions used in a recent paper (https://arxiv.org/abs/2210.02905). This PR includes the acquisition function and the necessary utilities. I have included a notebook that describes how to use these methods.

I was not sure what were the best places to add these acquisition functions, so I put them all in the multi-objective folder. Nevertheless, they should work for single-objective optimization as well.

Thanks,
Ben

Pull Request resolved: #1458

Reviewed By: sdaulton

Differential Revision: D41125110

Pulled By: esantorella

fbshipit-source-id: d301c659246dfff2ceee45d1905fdc578bd4b737

Author: benmltu

botorch/acquisition/joint_entropy_search.py

@@ -0,0 +1,111 @@
+#!/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"""
+Acquisition function for joint entropy search (JES). The code utilizes the
+implementation designed for the multi-objective batch setting.
+
+"""
+
+from __future__ import annotations
+
+from typing import Any, Optional
+
+from botorch.acquisition.multi_objective.joint_entropy_search import (
+    qLowerBoundMultiObjectiveJointEntropySearch,
+)
+from botorch.acquisition.multi_objective.utils import compute_sample_box_decomposition
+from botorch.models.model import Model
+from botorch.utils.transforms import concatenate_pending_points, t_batch_mode_transform
+from torch import Tensor
+
+
+class qLowerBoundJointEntropySearch(qLowerBoundMultiObjectiveJointEntropySearch):
+    r"""The acquisition function for the Joint Entropy Search, where the batches
+    `q > 1` are supported through the lower bound formulation.
+
+    This acquisition function computes the mutual information between the observation
+    at a candidate point `X` and the optimal input-output pair.
+
+    See [Tu2022]_ for a discussion on the estimation procedure.
+
+    NOTES:
+    (i) The estimated acquisition value could be negative.
+
+    (ii) The lower bound batch acquisition function might not be monotone in the
+    sense that adding more elements to the batch does not necessarily increase the
+    acquisition value. Specifically, the acquisition value can become smaller when
+    more inputs are added.
+    """
+
+    def __init__(
+        self,
+        model: Model,
+        optimal_inputs: Tensor,
+        optimal_outputs: Tensor,
+        maximize: bool = True,
+        hypercell_bounds: Tensor = None,
+        X_pending: Optional[Tensor] = None,
+        estimation_type: str = "LB",
+        num_samples: int = 64,
+        **kwargs: Any,
+    ) -> None:
+        r"""Joint entropy search acquisition function.
+
+        Args:
+            model: A fitted single-outcome model.
+            optimal_inputs: A `num_samples x d`-dim tensor containing the sampled
+                optimal inputs of dimension `d`. We assume for simplicity that each
+                sample only contains one optimal set of inputs.
+            optimal_outputs: A `num_samples x 1`-dim Tensor containing the optimal
+                set of objectives of dimension `1`.
+            maximize: If true, we consider a maximization problem.
+            hypercell_bounds:  A `num_samples x 2 x J x 1`-dim Tensor containing the
+                hyper-rectangle bounds for integration, where `J` is the number of
+                hyper-rectangles. By default, the problem is assumed to be
+                unconstrained and therefore the region of integration for a sample
+                `(x*, y*)` is a `J=1` hyper-rectangle of the form  `(-infty, y^*]`
+                for a maximization problem and `[y^*, +infty)` for a minimization
+                problem. In the constrained setting, the region of integration also
+                includes the infeasible space.
+            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.
+            estimation_type: A string to determine which entropy estimate is
+                computed: "0", "LB", "LB2", or "MC". In the single-objective
+                setting, "LB" is equivalent to "LB2".
+            num_samples: The number of Monte Carlo samples used for the Monte Carlo
+                estimate.
+        """
+        if hypercell_bounds is None:
+            hypercell_bounds = compute_sample_box_decomposition(
+                pareto_fronts=optimal_outputs.unsqueeze(-2), maximize=maximize
+            )
+
+        super().__init__(
+            model=model,
+            pareto_sets=optimal_inputs.unsqueeze(-2),
+            pareto_fronts=optimal_outputs.unsqueeze(-2),
+            hypercell_bounds=hypercell_bounds,
+            X_pending=X_pending,
+            estimation_type=estimation_type,
+            num_samples=num_samples,
+        )
+
+    @concatenate_pending_points
+    @t_batch_mode_transform()
+    def forward(self, X: Tensor) -> Tensor:
+        r"""Evaluates qLowerBoundJointEntropySearch at the design points `X`.
+
+        Args:
+            X: A `batch_shape x q x d`-dim Tensor of `batch_shape` t-batches with `q`
+            `d`-dim design points each.
+
+        Returns:
+            A `batch_shape`-dim Tensor of acquisition values at the given design
+            points `X`.
+        """
+
+        return self._compute_lower_bound_information_gain(X)