Improvement of qBayesianActiveLearningByDisagreement (#2457)

Summary:
Pull Request resolved: #2457

Improvement of the implementation of qBayesianActiveLearningByDisagreement
- Utilizes a Monte Carlo approach for approximating the entropy
- Does not use concatenate_pending_points, as it is not evident that fantasizing makes sense in the same way as for standard MC acquisition functions
- Can accept posterior transforms

- get_model and get_fully_bayesian_model are used in tests to be similar to other tests (e.g. JES & the subsequent active learning acqfs to enable move to test_helpers

Differential Revision: D60308502

botorch/acquisition/bayesian_active_learning.py

@@ -24,8 +24,11 @@
 
 import torch
 from botorch.acquisition.acquisition import AcquisitionFunction, MCSamplerMixin
-from botorch.models.fully_bayesian import SaasFullyBayesianSingleTaskGP
+from botorch.acquisition.objective import PosteriorTransform
+from botorch.models.fully_bayesian import MCMC_DIM, SaasFullyBayesianSingleTaskGP
 from botorch.models.model import Model
+from botorch.sampling.base import MCSampler
+from botorch.sampling.normal import SobolQMCNormalSampler
 from botorch.utils.transforms import concatenate_pending_points, t_batch_mode_transform
 from torch import Tensor
 
@@ -54,19 +57,33 @@ class qBayesianActiveLearningByDisagreement(
     def __init__(
         self,
         model: SaasFullyBayesianSingleTaskGP,
+        sampler: Optional[MCSampler] = None,
+        posterior_transform: Optional[PosteriorTransform] = None,
         X_pending: Optional[Tensor] = None,
     ) -> None:
         """
         Batch implementation [kirsch2019batchbald]_ of BALD [Houlsby2011bald]_,
         which maximizes the mutual information between the next observation and the
-        hyperparameters of the model. Computed by informational lower bound.
+        hyperparameters of the model. Computed by Monte Carlo integration.
 
         Args:
-            model: A fully bayesian single-outcome model.
-            X_pending: A `batch_shape, m x d`-dim Tensor of `m` design points.
+            model: A fully bayesian model (SaasFullyBayesianSingleTaskGP).
+            sampler: The sampler used for drawing samples to approximate the entropy
+                of the Gaussian Mixture posterior.
+            posterior_transform: A PosteriorTransform. If using a multi-output model,
+                a PosteriorTransform that transforms the multi-output posterior into a
+                single-output posterior is required.
+            X_pending: A `batch_shape x m x d`-dim Tensor of `m` design points
+
         """
         super().__init__(model)
+
+        if sampler is None:
+            self.sampler = SobolQMCNormalSampler(sample_shape=torch.Size([64]))
+        else:
+            self.sampler = sampler
         self.set_X_pending(X_pending)
+        self.posterior_transform = posterior_transform
 
     @concatenate_pending_points
     @t_batch_mode_transform()
@@ -79,23 +96,62 @@ def forward(self, X: Tensor) -> Tensor:
         Returns:
             A `batch_shape x num_models`-dim Tensor of BALD values.
         """
-        return self._compute_lower_bound_information_gain(X)
-
-    def _compute_lower_bound_information_gain(self, X: Tensor) -> Tensor:
-        r"""Evaluates the lower bounded information gain on the candidate set `X`.
+        return (
+            qBayesianActiveLearningByDisagreement._compute_monte_carlo_information_gain(
+                X, self.model, self.sampler, self.posterior_transform
+            )
+        )
+
+    @staticmethod
+    def _compute_monte_carlo_information_gain(
+        X: Tensor,
+        model: Model,
+        sampler: MCSampler,
+        posterior_transform: Optional[PosteriorTransform] = None,
+    ) -> Tensor:
+        posterior = model.posterior(
+            X, observation_noise=True, posterior_transform=posterior_transform
+        )
+        r"""Evaluate the monte carlo-estimated information gain over a Gaussian Mixture
+        marginal posterior, and the Gaussian conditional posterior to obtain the
+        qBayesianActiveLearningByDisagreement on the candidate set `X`.
 
         Args:
             X: `batch_shape x q x D`-dim Tensor of input points.
+            model: A fully bayesian model (SaasFullyBayesianSingleTaskGP).
+            sampler: The MCSampler used for drawing samples to approximate the entropy.
+            posterior_transform: A PosteriorTransform (optional).
 
         Returns:
-            A `batch_shape x num_models`-dim Tensor of information gains.
+            A `batch_shape x num_models`-dim Tensor of BALD values.
         """
-        posterior = self.model.posterior(X, observation_noise=True)
-        marg_covar = posterior.mixture_covariance_matrix
-        cond_variances = posterior.variance
-
-        prev_entropy = torch.logdet(marg_covar).unsqueeze(-1)
-        # squeeze excess dim and mean over q-batch
-        post_ub_entropy = torch.log(cond_variances).squeeze(-1).mean(-1)
-
-        return prev_entropy - post_ub_entropy
+        # draw samples from the mixture posterior.
+        # samples: num_samples x batch_shape x num_models x q x num_outputs
+        samples = sampler(posterior)
+
+        # Estimate the entropy of 'num_samples' samples from 'num_models' models by
+        # evaluating the log_prob on each sample on the mixture posterior
+        # (which constitutes of M models). thus, order N*M^2 computations
+
+        # Make room and move the model dim to the front, squeeze the num_outputs dim.
+        # prev_samples: num_models x num_samples x batch_shape x 1 x q
+        prev_samples = samples.unsqueeze(0).transpose(0, MCMC_DIM).squeeze(-1)
+
+        # avg the probs over models in the mixture - dim (-2) will be broadcasted
+        # with the num_models of the posterior --> querying all samples on all models
+        # posterior.mvn takes q-dimensional input by default, which removes the q-dim
+        # component_sample_probs: num_models x num_samples x batch_shape x num_models
+        component_sample_probs = posterior.mvn.log_prob(prev_samples).exp()
+
+        # average over mixture components
+        mixture_sample_probs = component_sample_probs.mean(dim=-1)
+
+        # this is the average over the model and sample dim
+        prev_entropy = -mixture_sample_probs.log().mean(
+            dim=[0, 1],
+        )
+
+        # the posterior entropy is an average entropy over gaussians, so no mixture
+        post_entropy = -posterior.mvn.log_prob(samples.squeeze(-1)).mean(0)
+        bald = prev_entropy.unsqueeze(-1) - post_entropy
+        return bald

botorch/acquisition/input_constructors.py

@@ -1678,9 +1678,13 @@ def construct_inputs_qJES(
 def construct_inputs_BALD(
     model: Model,
     X_pending: Optional[Tensor] = None,
+    sampler: Optional[MCSampler] = None,
+    posterior_transform: Optional[PosteriorTransform] = None,
 ):
     inputs = {
         "model": model,
         "X_pending": X_pending,
+        "sampler": sampler,
+        "posterior_transform": posterior_transform,
     }
     return inputs

test/acquisition/test_bayesian_active_learning.py

@@ -13,9 +13,32 @@
 from botorch.models import SingleTaskGP
 from botorch.models.fully_bayesian import SaasFullyBayesianSingleTaskGP
 from botorch.models.transforms.outcome import Standardize
+from botorch.sampling.normal import IIDNormalSampler, SobolQMCNormalSampler
 from botorch.utils.testing import BotorchTestCase
 
 
+def get_model(
+    train_X,
+    train_Y,
+    standardize_model,
+    **tkwargs,
+):
+    num_objectives = train_Y.shape[-1]
+
+    if standardize_model:
+        outcome_transform = Standardize(m=num_objectives)
+    else:
+        outcome_transform = None
+
+    model = SingleTaskGP(
+        train_X=train_X,
+        train_Y=train_Y,
+        outcome_transform=outcome_transform,
+    )
+
+    return model
+
+
 def _get_mcmc_samples(num_samples: int, dim: int, infer_noise: bool, **tkwargs):
 
     mcmc_samples = {
@@ -28,7 +51,7 @@ def _get_mcmc_samples(num_samples: int, dim: int, infer_noise: bool, **tkwargs):
     return mcmc_samples
 
 
-def get_model(
+def get_fully_bayesian_model(
     train_X,
     train_Y,
     num_models,
@@ -72,21 +95,26 @@ def test_q_bayesian_active_learning_by_disagreement(self):
         tkwargs = {"device": self.device}
         num_objectives = 1
         num_models = 3
+        input_dim = 2
+
+        X_pending_list = [None, torch.rand(2, input_dim)]
         for (
             dtype,
             standardize_model,
             infer_noise,
+            X_pending,
         ) in product(
             (torch.float, torch.double),
             (False, True),  # standardize_model
             (True,),  # infer_noise - only one option avail in PyroModels
+            X_pending_list,
         ):
+            X_pending = X_pending.to(**tkwargs) if X_pending is not None else None
             tkwargs["dtype"] = dtype
-            input_dim = 2
             train_X = torch.rand(4, input_dim, **tkwargs)
             train_Y = torch.rand(4, num_objectives, **tkwargs)
 
-            model = get_model(
+            model = get_fully_bayesian_model(
                 train_X,
                 train_Y,
                 num_models,
@@ -96,32 +124,40 @@ def test_q_bayesian_active_learning_by_disagreement(self):
             )
 
             # test acquisition
-            X_pending_list = [None, torch.rand(2, input_dim, **tkwargs)]
-            for i in range(len(X_pending_list)):
-                X_pending = X_pending_list[i]
-
-                acq = qBayesianActiveLearningByDisagreement(
-                    model=model,
-                    X_pending=X_pending,
-                )
-
-                test_Xs = [
-                    torch.rand(4, 1, input_dim, **tkwargs),
-                    torch.rand(4, 3, input_dim, **tkwargs),
-                    torch.rand(4, 5, 1, input_dim, **tkwargs),
-                    torch.rand(4, 5, 3, input_dim, **tkwargs),
-                ]
-
-                for j in range(len(test_Xs)):
-                    acq_X = acq.forward(test_Xs[j])
-                    acq_X = acq(test_Xs[j])
-                    # assess shape
-                    self.assertTrue(acq_X.shape == test_Xs[j].shape[:-2])
+            acq = qBayesianActiveLearningByDisagreement(
+                model=model,
+                X_pending=X_pending,
+            )
+            self.assertIsInstance(acq.sampler, SobolQMCNormalSampler)
+
+            acq2 = qBayesianActiveLearningByDisagreement(
+                model=model, sampler=IIDNormalSampler(torch.Size([9]))
+            )
+            self.assertIsInstance(acq2.sampler, IIDNormalSampler)
+
+            test_Xs = [
+                torch.rand(4, 1, input_dim, **tkwargs),
+                torch.rand(4, 3, input_dim, **tkwargs),
+                torch.rand(4, 5, 1, input_dim, **tkwargs),
+                torch.rand(4, 5, 3, input_dim, **tkwargs),
+                torch.rand(5, 13, input_dim, **tkwargs),
+            ]
+
+            for j in range(len(test_Xs)):
+                acq_X = acq.forward(test_Xs[j])
+                acq_X = acq(test_Xs[j])
+                # assess shape
+                self.assertTrue(acq_X.shape == test_Xs[j].shape[:-2])
+
+                self.assertTrue(torch.all(acq_X > 0))
 
         # Support with non-fully bayesian models is not possible. Thus, we
         # throw an error.
-        non_fully_bayesian_model = SingleTaskGP(train_X, train_Y)
-        with self.assertRaises(ValueError):
+        with self.assertRaisesRegex(
+            ValueError,
+            "Fully Bayesian acquisition functions require a SaasFullyBayesianSingleTaskGP to run.",
+        ):
+            non_fully_bayesian_model = get_model(train_X, train_Y, False)
             acq = qBayesianActiveLearningByDisagreement(
                 model=non_fully_bayesian_model,
             )