Improvement of optimize_posterior_samples and get_optimal_samples to

improve info-theoretic acquisition functions.

Author: hvarfner

botorch/acquisition/utils.py

@@ -534,6 +534,7 @@ def get_optimal_samples(
     posterior_transform: ScalarizedPosteriorTransform | None = None,
     objective: MCAcquisitionObjective | None = None,
     return_transformed: bool = False,
+    options: dict | None = None,
 ) -> tuple[Tensor, Tensor]:
     """Draws sample paths from the posterior and maximizes the samples using GD.
 
@@ -551,7 +552,8 @@ def get_optimal_samples(
         objective: An MCAcquisitionObjective, used to negate the objective or otherwise
             transform sample outputs. Cannot be combined with `posterior_transform`.
         return_transformed: If True, return the transformed samples.
-
+        options: Options for generation of initial candidates, passed to
+            gen_batch_initial_conditions.
     Returns:
         The optimal input locations and corresponding outputs, x* and f*.
 
@@ -576,12 +578,20 @@ def get_optimal_samples(
         sample_transform = None
 
     paths = get_matheron_path_model(model=model, sample_shape=torch.Size([num_optima]))
+    suggested_points = prune_inferior_points(
+        model=model,
+        X=model.train_inputs[0],
+        posterior_transform=posterior_transform,
+        objective=objective,
+    )
     optimal_inputs, optimal_outputs = optimize_posterior_samples(
         paths=paths,
         bounds=bounds,
         raw_samples=raw_samples,
         num_restarts=num_restarts,
         sample_transform=sample_transform,
         return_transformed=return_transformed,
+        suggested_points=suggested_points,
+        options=options,
     )
     return optimal_inputs, optimal_outputs

botorch/utils/sampling.py

@@ -999,10 +999,12 @@ def sparse_to_dense_constraints(
 def optimize_posterior_samples(
     paths: GenericDeterministicModel,
     bounds: Tensor,
-    raw_samples: int = 1024,
-    num_restarts: int = 20,
+    raw_samples: int = 2048,
+    num_restarts: int = 4,
     sample_transform: Callable[[Tensor], Tensor] | None = None,
     return_transformed: bool = False,
+    suggested_points: Tensor | None = None,
+    options: dict | None = None,
 ) -> tuple[Tensor, Tensor]:
     r"""Cheaply maximizes posterior samples by random querying followed by
     gradient-based optimization using SciPy's L-BFGS-B routine.
@@ -1011,19 +1013,27 @@ def optimize_posterior_samples(
         paths: Random Fourier Feature-based sample paths from the GP
         bounds: The bounds on the search space.
         raw_samples: The number of samples with which to query the samples initially.
+            Raw samples are cheap to evaluate, so this should ideally be set much higher
+            than num_restarts.
         num_restarts: The number of points selected for gradient-based optimization.
+            Should be set low relative to the number of raw samples for time-efficiency.
         sample_transform: A callable transform of the sample outputs (e.g.
             MCAcquisitionObjective or ScalarizedPosteriorTransform.evaluate) used to
             negate the objective or otherwise transform the output.
         return_transformed: A boolean indicating whether to return the transformed
             or non-transformed samples.
+        suggested_points: Tensor of suggested input locations that are high-valued.
+            These are more densely evaluated during the sampling phase of optimization.
+        options: Options for generation of initial candidates, passed to
+            gen_batch_initial_conditions.
 
     Returns:
         A two-element tuple containing:
             - X_opt: A `num_optima x [batch_size] x d`-dim tensor of optimal inputs x*.
             - f_opt: A `num_optima x [batch_size] x m`-dim, optionally
                 `num_optima x [batch_size] x 1`-dim,  tensor of optimal outputs f*.
     """
+    options = {} if options is None else options
 
     def path_func(x) -> Tensor:
         res = paths(x)
@@ -1032,21 +1042,35 @@ def path_func(x) -> Tensor:
 
         return res.squeeze(-1)
 
-    candidate_set = unnormalize(
-        SobolEngine(dimension=bounds.shape[1], scramble=True).draw(n=raw_samples),
-        bounds=bounds,
-    )
     # queries all samples on all candidates - output shape
     # raw_samples * num_optima * num_models
+    frac_random = 1 if suggested_points is None else options.get("frac_random", 0.9)
+    candidate_set = draw_sobol_samples(
+        bounds=bounds, n=round(raw_samples * frac_random), q=1
+    ).squeeze(-2)
+    if frac_random < 1:
+        perturbed_suggestions = sample_truncated_normal_perturbations(
+            X=suggested_points,
+            n_discrete_points=round(raw_samples * (1 - frac_random)),
+            sigma=options.get("sample_around_best_sigma", 1e-2),
+            bounds=bounds,
+        )
+        candidate_set = torch.cat((candidate_set, perturbed_suggestions))
+
     candidate_queries = path_func(candidate_set)
-    argtop_k = torch.topk(candidate_queries, num_restarts, dim=-1).indices
-    X_top_k = candidate_set[argtop_k, :]
+    idx = boltzmann_sample(
+        function_values=candidate_queries.unsqueeze(-1),
+        num_samples=num_restarts,
+        eta=options.get("eta", 2.0),
+        replacement=False,
+    )
+    ics = candidate_set[idx, :]
 
     # to avoid circular import, the import occurs here
     from botorch.generation.gen import gen_candidates_scipy
 
     X_top_k, f_top_k = gen_candidates_scipy(
-        X_top_k,
+        ics,
         path_func,
         lower_bounds=bounds[0],
         upper_bounds=bounds[1],
@@ -1101,8 +1125,9 @@ def boltzmann_sample(
         eta *= temp_decrease
         weights = torch.exp(eta * norm_weights)
 
+    # squeeze in case of m = 1 (mono-output provided as batch_size x N x 1)
     return batched_multinomial(
-        weights=weights, num_samples=num_samples, replacement=replacement
+        weights=weights.squeeze(-1), num_samples=num_samples, replacement=replacement
     )
 
 

test/acquisition/test_utils.py

@@ -33,6 +33,7 @@
     UnsupportedError,
 )
 from botorch.models import SingleTaskGP
+from botorch.utils.test_helpers import get_fully_bayesian_model, get_model
 from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
 from gpytorch.distributions import MultivariateNormal
 
@@ -413,17 +414,14 @@ def test_project_to_sample_points(self):
 
 
 class TestGetOptimalSamples(BotorchTestCase):
-    def test_get_optimal_samples(self):
-        dims = 3
-        dtype = torch.float64
+    def _test_get_optimal_samples_base(self, model):
+        dims = model.train_inputs[0].shape[1]
+        dtype = model.train_targets.dtype
+        batch_shape = model.batch_shape
         for_testing_speed_kwargs = {"raw_samples": 20, "num_restarts": 2}
         num_optima = 7
-        batch_shape = (3,)
 
         bounds = torch.tensor([[0, 1]] * dims, dtype=dtype).T
-        X = torch.rand(*batch_shape, 4, dims, dtype=dtype)
-        Y = torch.sin(2 * 3.1415 * X).sum(dim=-1, keepdim=True).to(dtype)
-        model = SingleTaskGP(train_X=X, train_Y=Y)
         posterior_transform = ScalarizedPosteriorTransform(
             weights=torch.ones(1, dtype=dtype)
         )
@@ -438,6 +436,7 @@ def test_get_optimal_samples(self):
                 num_optima=num_optima,
                 **for_testing_speed_kwargs,
             )
+
         correct_X_shape = (num_optima,) + batch_shape + (dims,)
         correct_f_shape = (num_optima,) + batch_shape + (1,)
         self.assertEqual(X_opt_def.shape, correct_X_shape)
@@ -519,6 +518,22 @@ def test_get_optimal_samples(self):
                 **for_testing_speed_kwargs,
             )
 
+    def test_optimal_samples(self):
+        dims = 3
+        dtype = torch.float64
+        X = torch.rand(4, dims, dtype=dtype)
+        Y = torch.sin(2 * 3.1415 * X).sum(dim=-1, keepdim=True).to(dtype)
+        model = get_model(train_X=X, train_Y=Y)
+        self._test_get_optimal_samples_base(model)
+        fully_bayesian_model = get_fully_bayesian_model(
+            train_X=X,
+            train_Y=Y,
+            num_models=4,
+            standardize_model=True,
+            infer_noise=True,
+        )
+        self._test_get_optimal_samples_base(fully_bayesian_model)
+
 
 class TestPreferenceUtils(BotorchTestCase):
     def test_repeat_to_match_aug_dim(self):

test/utils/test_sampling.py

@@ -578,9 +578,13 @@ def test_optimize_posterior_samples(self):
         dims = 2
         dtype = torch.float64
         eps = 1e-4
-        for_testing_speed_kwargs = {"raw_samples": 128, "num_restarts": 4}
-        nums_optima = (1, 7)
-        batch_shapes = ((), (2,), (3, 2))
+        for_testing_speed_kwargs = {
+            "raw_samples": 64,
+            "num_restarts": 2,
+            "options": {"eta": 10},
+        }
+        nums_optima = (1, 5)
+        batch_shapes = ((), (3,))
         posterior_transforms = (
             None,
             ScalarizedPosteriorTransform(weights=-torch.ones(1, dtype=dtype)),
@@ -589,16 +593,19 @@ def test_optimize_posterior_samples(self):
             nums_optima, batch_shapes, posterior_transforms
         ):
             bounds = torch.tensor([[0, 1]] * dims, dtype=dtype).T
-            X = torch.rand(*batch_shape, 4, dims, dtype=dtype)
+            X = torch.rand(*batch_shape, 3, dims, dtype=dtype)
             Y = torch.pow(X - 0.5, 2).sum(dim=-1, keepdim=True)
 
             # having a noiseless model all but guarantees that the found optima
             # will be better than the observations
-            model = SingleTaskGP(X, Y, torch.full_like(Y, eps))
+            model = SingleTaskGP(
+                train_X=X, train_Y=Y, train_Yvar=torch.full_like(Y, eps)
+            )
             model.covar_module.lengthscale = 0.5
             paths = get_matheron_path_model(
                 model=model, sample_shape=torch.Size([num_optima])
             )
+
             X_opt, f_opt = optimize_posterior_samples(
                 paths=paths,
                 bounds=bounds,
@@ -616,8 +623,6 @@ def test_optimize_posterior_samples(self):
             self.assertTrue(torch.all(X_opt >= bounds[0]))
             self.assertTrue(torch.all(X_opt <= bounds[1]))
 
-            # Check that the all found optima are larger than the observations
-            # This is not 100% deterministic, but just about.
             Y_queries = paths(X)
             # this is when we negate, so the values should be smaller
             if posterior_transform:
@@ -642,7 +647,7 @@ def test_optimize_posterior_samples_multi_objective(self):
         dims = 2
         dtype = torch.float64
         eps = 1e-4
-        for_testing_speed_kwargs = {"raw_samples": 128, "num_restarts": 4}
+        for_testing_speed_kwargs = {"raw_samples": 64, "num_restarts": 2}
         num_optima = 5
         batch_shape = (3,)