Hyperparameter-Informed Predictive Exploration

Carl Hvarfner · facebook-github-bot · commit 1c0e0ab797b0 · 2025-12-03T15:39:12.000-08:00
Summary:
Added HIPE to `botorch_community`. N8602849 is the accompanying tutorial notebook. Could certainly go into botorch as well.


Notebook is still WIP, and the inconvenient passing of q and `bounds` into the acuisition function is unconventional. Ideally, this could be pre-computed at acquisition function optimization time, when these args are usually passed. Feedback on these aspects would be very welcomed.

Differential Revision: D87000239
diff --git a/botorch_community/acquisition/__init__.py b/botorch_community/acquisition/__init__.py
@@ -6,6 +6,7 @@
 from botorch_community.acquisition.bayesian_active_learning import (
     qBayesianQueryByComittee,
     qBayesianVarianceReduction,
+    qHyperparameterInformedPredictiveExploration,
     qStatisticalDistanceActiveLearning,
 )
 
@@ -23,6 +24,7 @@
     "LogRegionalExpectedImprovement",
     "qBayesianQueryByComittee",
     "qBayesianVarianceReduction",
+    "qHyperparameterInformedPredictiveExploration",
     "qLogRegionalExpectedImprovement",
     "qSelfCorrectingBayesianOptimization",
     "qStatisticalDistanceActiveLearning",
diff --git a/botorch_community/acquisition/bayesian_active_learning.py b/botorch_community/acquisition/bayesian_active_learning.py
@@ -33,13 +33,21 @@
 
 from __future__ import annotations
 
-from typing import Optional
+import math
+
+from typing import Literal, Optional
 
 import torch
+from botorch.acquisition.acquisition import MCSamplerMixin
 from botorch.acquisition.bayesian_active_learning import (
     FullyBayesianAcquisitionFunction,
+    qBayesianActiveLearningByDisagreement,
 )
+from botorch.acquisition.objective import PosteriorTransform
 from botorch.models.fully_bayesian import MCMC_DIM, SaasFullyBayesianSingleTaskGP
+from botorch.optim import optimize_acqf
+from botorch.sampling.base import MCSampler
+from botorch.utils.sampling import draw_sobol_samples
 from botorch.utils.transforms import (
     average_over_ensemble_models,
     concatenate_pending_points,
@@ -51,6 +59,7 @@
 
 
 SAMPLE_DIM = -4
+TWO_PI_E = 2 * math.pi * math.e
 DISTANCE_METRICS = {
     "hellinger": mvn_hellinger_distance,
     "kl_divergence": mvn_kl_divergence,
@@ -159,3 +168,189 @@ def forward(self, X: Tensor) -> Tensor:
         # squeeze output dim - batch dim computed and reduced inside of dist
         # MCMC dim is averaged in decorator
         return dist.squeeze(-1)
+
+
+class qExpectedPredictiveInformationGain(FullyBayesianAcquisitionFunction):
+    def __init__(
+        self,
+        model: SaasFullyBayesianSingleTaskGP,
+        mc_points: Tensor,
+        X_pending: Tensor | None = None,
+    ) -> None:
+        """Expected predictive information gain for active learning.
+
+        Computes the mutual information between candidate queries and a test set
+        (typically MC samples over the design space).
+
+        Args:
+            model: A fully bayesian model (SaasFullyBayesianSingleTaskGP).
+            mc_points: A `N x d` tensor of points to use for MC-integrating the
+                posterior entropy (test set).
+            X_pending: A `m x d`-dim Tensor of `m` design points.
+        """
+        super().__init__(model)
+        if mc_points.ndim != 2:
+            raise ValueError(
+                f"mc_points must be a 2-dimensional tensor, but got shape "
+                f"{mc_points.shape}"
+            )
+        self.register_buffer("mc_points", mc_points)
+        self.set_X_pending(X_pending)
+
+    @concatenate_pending_points
+    @t_batch_mode_transform()
+    @average_over_ensemble_models
+    def forward(self, X: Tensor) -> Tensor:
+        """Evaluate test set information gain.
+
+        Args:
+            X: A `batch_shape x q x d`-dim Tensor of input points.
+
+        Returns:
+            A Tensor of information gain values.
+        """
+        # Get the posterior for the candidate points
+        posterior = self.model.posterior(X, observation_noise=True)
+        noise = (
+            posterior.variance
+            - self.model.posterior(X, observation_noise=False).variance
+        )
+        cond_Y = posterior.mean
+
+        # Condition the model on the candidate observations
+        cond_X = X.unsqueeze(-3).expand(*[cond_Y.shape[:-1] + X.shape[-1:]])
+        conditional_model = self.model.condition_on_observations(
+            X=cond_X,
+            Y=cond_Y,
+            noise=noise,
+        )
+
+        # Evaluate posterior variance at test set with and without conditioning
+        uncond_var = self.model.posterior(
+            self.mc_points, observation_noise=True
+        ).variance
+        cond_var = conditional_model.posterior(
+            self.mc_points, observation_noise=True
+        ).variance
+
+        # Compute information gain as reduction in entropy
+        prev_entropy = torch.log(uncond_var * TWO_PI_E).sum(-1) / 2
+        post_entropy = torch.log(cond_var * TWO_PI_E).sum(-1) / 2
+        return (prev_entropy - post_entropy).mean(-1)
+
+
+class qHyperparameterInformedPredictiveExploration(
+    FullyBayesianAcquisitionFunction, MCSamplerMixin
+):
+    def __init__(
+        self,
+        model: SaasFullyBayesianSingleTaskGP,
+        mc_points: Tensor,
+        bounds: Tensor,
+        sampler: MCSampler | None = None,
+        posterior_transform: PosteriorTransform | None = None,
+        X_pending: Tensor | None = None,
+        num_samples: int = 512,
+        beta: float | None = None,
+        beta_tuning_method: Literal["sobol", "optimize"] = "sobol",
+    ) -> None:
+        """Hyperparameter-informed Predictive Exploration acquisition function.
+
+        This acquisition function combines the mutual information between the
+        subsequent queries and a test set (predictive information gain) with the
+        mutual information between observations and hyperparameters (BALD), weighted
+        by a tuning factor. This balances exploration of the design space with
+        reduction of hyperparameter uncertainty.
+
+        The acquisition function is computed as:
+            beta * BALD + TSIG
+        where beta is either provided or automatically tuned.
+
+        Args:
+            model: A fully bayesian model (SaasFullyBayesianSingleTaskGP).
+            mc_points: A `N x d` tensor of points to use for MC-integrating the
+                posterior entropy (test set). Usually, these are qMC samples on
+                the whole design space.
+            bounds: A `2 x d` tensor of bounds for the design space, used for
+                beta tuning.
+            sampler: The sampler used for drawing samples to approximate the entropy
+                of the Gaussian Mixture posterior. If None, uses default sampler.
+            X_pending: A `m x d`-dim Tensor of `m` design points that have been
+                submitted for evaluation but have not yet been observed.
+            num_samples: Number of samples to use for MC estimation of entropy.
+            beta: Fixed tuning factor. If None, it will be automatically computed
+                on the first forward pass based on the batch size q.
+            beta_tuning_method: Method for tuning beta. Options are "optimize"
+                (optimize acquisition function to find beta) or "sobol" (use sobol
+                samples). Only used when beta is None.
+        """
+        super().__init__(model=model)
+        MCSamplerMixin.__init__(self)
+        if mc_points.ndim != 2:
+            raise ValueError(
+                f"mc_points must be a 2-dimensional tensor, but got shape "
+                f"{mc_points.shape}"
+            )
+        self.set_X_pending(X_pending)
+        self.num_samples = num_samples
+        self.beta_tuning_method = beta_tuning_method
+        self.register_buffer("mc_points", mc_points)
+        self.register_buffer("bounds", bounds)
+        self.sampler = sampler
+        self.posterior_transform = posterior_transform
+        self._tuning_factor: float | None = beta
+        self._tuning_factor_q: int | None = None
+
+    def _compute_tuning_factor(self, q: int) -> None:
+        """Compute the tuning factor beta for weighting BALD vs TSIG."""
+        if self.beta_tuning_method == "sobol":
+            draws = draw_sobol_samples(
+                bounds=self.bounds,
+                q=q,
+                n=1,
+            ).squeeze(0)
+            # Compute the ratio at sobol samples
+            tsig_val = qExpectedPredictiveInformationGain.forward(
+                self,
+                draws,
+            )
+            bald_val = qBayesianActiveLearningByDisagreement.forward(self, draws)
+            self._tuning_factor = (tsig_val / (bald_val + 1e-8)).mean().item()
+        elif self.beta_tuning_method == "optimize":
+            # Optimize to find the best tuning factor
+            bald_acqf = qBayesianActiveLearningByDisagreement(
+                model=self.model,
+                sampler=self.sampler,
+            )
+            _, bald_val = optimize_acqf(
+                bald_acqf,
+                bounds=self.bounds,
+                q=q,
+                num_restarts=1,
+                raw_samples=128,
+                options={"batch_limit": 16},
+            )
+            self._tuning_factor = bald_val.mean().item()
+        self._tuning_factor_q = q
+
+    @concatenate_pending_points
+    @t_batch_mode_transform()
+    def forward(self, X: Tensor) -> Tensor:
+        """Evaluate the acquisition function at X.
+
+        Args:
+            X: A `batch_shape x q x d`-dim Tensor of input points.
+
+        Returns:
+            A `batch_shape`-dim Tensor of acquisition values.
+        """
+        q = X.shape[-2]
+        # Compute tuning factor if not set or if q has changed
+        if self._tuning_factor is None or self._tuning_factor_q != q:
+            self._compute_tuning_factor(q)
+
+        tsig = qExpectedPredictiveInformationGain.forward(self, X)
+        bald = qBayesianActiveLearningByDisagreement.forward(self, X)
+        # Since both acquisition functions are averaged over the ensemble,
+        # we do not average over the ensemble again here.
+        return self._tuning_factor * bald + tsig
diff --git a/test_community/acquisition/test_bayesian_active_learning.py b/test_community/acquisition/test_bayesian_active_learning.py
@@ -7,11 +7,14 @@
 from itertools import product
 
 import torch
+from botorch.utils.sampling import draw_sobol_samples
 from botorch.utils.test_helpers import get_fully_bayesian_model
 from botorch.utils.testing import BotorchTestCase
 from botorch_community.acquisition.bayesian_active_learning import (
     qBayesianQueryByComittee,
     qBayesianVarianceReduction,
+    qExpectedPredictiveInformationGain,
+    qHyperparameterInformedPredictiveExploration,
     qStatisticalDistanceActiveLearning,
 )
 
@@ -72,14 +75,112 @@ def test_q_statistical_distance_active_learning(self):
                     # assess shape
                     self.assertTrue(acq_X.shape == test_Xs[j].shape[:-2])
 
+
+class TestQExpectedPredictiveInformationGain(BotorchTestCase):
+    def test_q_expected_predictive_information_gain(self):
+        torch.manual_seed(1)
+        tkwargs = {"device": self.device, "dtype": torch.double}
+        input_dim = 2
+
+        model = get_fully_bayesian_model(
+            train_X=torch.rand(4, input_dim, **tkwargs),
+            train_Y=torch.rand(4, 1, **tkwargs),
+            num_models=3,
+            **tkwargs,
+        )
+        bounds = torch.tensor([[0.0] * input_dim, [1.0] * input_dim], **tkwargs)
+        mc_points = draw_sobol_samples(bounds=bounds, n=16, q=1).squeeze(-2)
+
+        acq = qExpectedPredictiveInformationGain(model=model, mc_points=mc_points)
+        test_X = torch.rand(4, 2, input_dim, **tkwargs)
+        acq_X = acq(test_X)
+        self.assertEqual(acq_X.shape, test_X.shape[:-2])
+        self.assertTrue((acq_X >= 0).all())
+
+        # test that mc_points must be 2-dimensional
         with self.assertRaises(ValueError):
-            acq = qStatisticalDistanceActiveLearning(
+            qExpectedPredictiveInformationGain(
                 model=model,
-                distance_metric="NOT_A_DISTANCE",
-                X_pending=X_pending,
+                mc_points=mc_points.unsqueeze(0),  # 3D tensor
             )
 
 
+class TestQHyperparameterInformedPredictiveExploration(BotorchTestCase):
+    def test_q_hyperparameter_informed_predictive_exploration(self):
+        torch.manual_seed(1)
+        tkwargs = {"device": self.device}
+        num_objectives = 1
+        num_models = 3
+        for (
+            dtype,
+            standardize_model,
+            infer_noise,
+        ) in product(
+            (torch.float, torch.double),
+            (False, True),
+            (True,),
+        ):
+            tkwargs["dtype"] = dtype
+            input_dim = 2
+            train_X = torch.rand(4, input_dim, **tkwargs)
+            train_Y = torch.rand(4, num_objectives, **tkwargs)
+
+            model = get_fully_bayesian_model(
+                train_X=train_X,
+                train_Y=train_Y,
+                num_models=num_models,
+                standardize_model=standardize_model,
+                infer_noise=infer_noise,
+                **tkwargs,
+            )
+
+            bounds = torch.tensor([[0.0] * input_dim, [1.0] * input_dim], **tkwargs)
+            mc_points = draw_sobol_samples(bounds=bounds, n=16, q=1).squeeze(-2)
+
+            # test with fixed beta
+            acq = qHyperparameterInformedPredictiveExploration(
+                model=model,
+                mc_points=mc_points,
+                bounds=bounds,
+                beta=1.0,
+            )
+
+            test_Xs = [
+                torch.rand(4, 1, input_dim, **tkwargs),
+                torch.rand(4, 3, input_dim, **tkwargs),
+            ]
+
+            for test_X in test_Xs:
+                acq_X = acq(test_X)
+                # assess shape
+                self.assertTrue(acq_X.shape == test_X.shape[:-2])
+                self.assertTrue((acq_X > 0).all())
+
+            # test beta tuning (beta=None) and re-tuning when q changes
+            for beta_tuning_method in ("sobol", "optimize"):
+                acq_tuned = qHyperparameterInformedPredictiveExploration(
+                    model=model,
+                    mc_points=mc_points,
+                    bounds=bounds,
+                    beta_tuning_method=beta_tuning_method,
+                )
+                # first forward pass computes tuning factor for q=1
+                acq_tuned(torch.rand(4, 1, input_dim, **tkwargs))
+                tuning_factor_q1 = acq_tuned._tuning_factor
+                # second forward pass with different q recomputes tuning factor
+                acq_tuned(torch.rand(4, 3, input_dim, **tkwargs))
+                tuning_factor_q3 = acq_tuned._tuning_factor
+                self.assertNotEqual(tuning_factor_q1, tuning_factor_q3)
+
+            # test that mc_points must be 2-dimensional
+            with self.assertRaises(ValueError):
+                qHyperparameterInformedPredictiveExploration(
+                    model=model,
+                    mc_points=mc_points.unsqueeze(0),  # 3D tensor
+                    bounds=bounds,
+                )
+
+
 class TestQBayesianQueryByComittee(BotorchTestCase):
     def test_q_bayesian_query_by_comittee(self):
         torch.manual_seed(1)
