[q]LogProbabilityOfFeasibility (#2815)

Summary:

This commit adds `LogProbabilityOfFeasibility` and the corresponding batch Monte-Carlo version `qLogProbabilityOfFeasibility`. These new acquisition functions compute a probability of feasibility acquisition value that is particularly relevant for optimization runs that start out without any feasible observations. After a feasible observation is found, the acquisition function likely becomes over-exploitative, and one is better served switching to an acquisition function that also takes into account the objective value, e.g. `qLogNEI`.

Differential Revision: D72411936

Author: SebastianAment

botorch/acquisition/analytic.py

@@ -13,7 +13,7 @@
 
 import math
 
-from abc import ABC
+from abc import ABC, abstractmethod
 from contextlib import nullcontext
 from copy import deepcopy
 
@@ -415,7 +415,112 @@ def forward(self, X: Tensor) -> Tensor:
         return _log_ei_helper(u) + sigma.log()
 
 
-class LogConstrainedExpectedImprovement(AnalyticAcquisitionFunction):
+class ConstrainedAnalyticAcquisitionFunctionMixin(ABC):
+    r"""Base class for constrained analytic acquisition functions."""
+
+    def __init__(
+        self,
+        constraints: dict[int, tuple[float | None, float | None]],
+    ) -> None:
+        r"""Analytic Log Probability of Feasibility.
+
+        Args:
+            model: A fitted multi-output model.
+            constraints: A dictionary of the form `{i: [lower, upper]}`, where
+                `i` is the output index, and `lower` and `upper` are lower and upper
+                bounds on that output (resp. interpreted as -Inf / Inf if None).
+        """
+        self.constraints = constraints
+        self._preprocess_constraint_bounds(constraints=constraints)
+
+    @abstractmethod
+    def register_buffer(self, name: str, value: Tensor) -> None:
+        """Add a buffer that can be accessed by `self.name` and stores the Tensor
+        `value`, usually provided by derivatives that also inherit from `nn.Module`.
+        """
+
+    def _preprocess_constraint_bounds(
+        self,
+        constraints: dict[int, tuple[float | None, float | None]],
+    ) -> None:
+        r"""Set up constraint bounds.
+
+        Args:
+            constraints: A dictionary of the form `{i: [lower, upper]}`, where
+                `i` is the output index, and `lower` and `upper` are lower and upper
+                bounds on that output (resp. interpreted as -Inf / Inf if None)
+        """
+        con_lower, con_lower_inds = [], []
+        con_upper, con_upper_inds = [], []
+        con_both, con_both_inds = [], []
+        con_indices = list(constraints.keys())
+        if len(con_indices) == 0:
+            raise ValueError("There must be at least one constraint.")
+        # CEI, LogCEI have an objective index, but LogPOF does not.
+        if hasattr(self, "objective_index") and self.objective_index in con_indices:
+            raise ValueError(
+                "Output corresponding to objective should not be a constraint."
+            )
+        for k in con_indices:
+            if constraints[k][0] is not None and constraints[k][1] is not None:
+                if constraints[k][1] <= constraints[k][0]:
+                    raise ValueError("Upper bound is less than the lower bound.")
+                con_both_inds.append(k)
+                con_both.append([constraints[k][0], constraints[k][1]])
+            elif constraints[k][0] is not None:
+                con_lower_inds.append(k)
+                con_lower.append(constraints[k][0])
+            elif constraints[k][1] is not None:
+                con_upper_inds.append(k)
+                con_upper.append(constraints[k][1])
+
+        for name, value in [
+            ("con_lower_inds", con_lower_inds),
+            ("con_upper_inds", con_upper_inds),
+            ("con_both_inds", con_both_inds),
+            ("con_both", con_both),
+            ("con_lower", con_lower),
+            ("con_upper", con_upper),
+        ]:
+            # tensor-based indexing is much faster than list-based advanced indexing
+            self.register_buffer(name, tensor=torch.as_tensor(value))
+
+    def _compute_log_prob_feas(
+        self,
+        means: Tensor,
+        sigmas: Tensor,
+    ) -> Tensor:
+        r"""Compute logarithm of the feasibility probability for each batch of X.
+
+        Args:
+            X: A `(b) x 1 x d`-dim Tensor of `(b)` t-batches of `d`-dim design
+                points each.
+            means: A `(b) x m`-dim Tensor of means.
+            sigmas: A `(b) x m`-dim Tensor of standard deviations.
+
+        Returns:
+            A `b`-dim tensor of log feasibility probabilities
+
+        Note: This function does case-work for upper bound, lower bound, and both-sided
+        bounds. Another way to do it would be to use 'inf' and -'inf' for the
+        one-sided bounds and use the logic for the both-sided case. But this
+        causes an issue with autograd since we get 0 * inf.
+        """
+        return compute_log_prob_feas_from_bounds(
+            con_lower_inds=self.con_lower_inds,
+            con_upper_inds=self.con_upper_inds,
+            con_both_inds=self.con_both_inds,
+            con_lower=self.con_lower,
+            con_upper=self.con_upper,
+            con_both=self.con_both,
+            means=means,
+            sigmas=sigmas,
+        )
+
+
+class LogConstrainedExpectedImprovement(
+    AnalyticAcquisitionFunction, ConstrainedAnalyticAcquisitionFunctionMixin
+):
     r"""Log Constrained Expected Improvement (feasibility-weighted).
 
     Computes the logarithm of the analytic expected improvement for a Normal posterior
@@ -464,13 +569,12 @@ def __init__(
             maximize: If True, consider the problem a maximization problem.
         """
         # Use AcquisitionFunction constructor to avoid check for posterior transform.
-        super(AnalyticAcquisitionFunction, self).__init__(model=model)
+        AcquisitionFunction.__init__(self, model=model)
         self.posterior_transform = None
         self.maximize = maximize
         self.objective_index = objective_index
-        self.constraints = constraints
         self.register_buffer("best_f", torch.as_tensor(best_f))
-        _preprocess_constraint_bounds(self, constraints=constraints)
+        ConstrainedAnalyticAcquisitionFunctionMixin.__init__(self, constraints)
         self.register_forward_pre_hook(convert_to_target_pre_hook)
 
     @t_batch_mode_transform(expected_q=1)
@@ -490,11 +594,77 @@ def forward(self, X: Tensor) -> Tensor:
         mean_obj, sigma_obj = means[..., ind], sigmas[..., ind]
         u = _scaled_improvement(mean_obj, sigma_obj, self.best_f, self.maximize)
         log_ei = _log_ei_helper(u) + sigma_obj.log()
-        log_prob_feas = _compute_log_prob_feas(self, means=means, sigmas=sigmas)
+        log_prob_feas = self._compute_log_prob_feas(means=means, sigmas=sigmas)
         return log_ei + log_prob_feas
 
 
-class ConstrainedExpectedImprovement(AnalyticAcquisitionFunction):
+class LogProbabilityOfFeasibility(
+    AnalyticAcquisitionFunction, ConstrainedAnalyticAcquisitionFunctionMixin
+):
+    r"""Log Probability of Feasbility.
+
+    Computes the logarithm of the analytic probability of feasibility for a Normal
+    posterior distribution weighted by a probability of feasibility. The objective and
+    constraints are assumed to be independent and have Gaussian posterior
+    distributions. Only supports non-batch mode (i.e. `q=1`). The model should be
+    multi-outcome, with the index of the objective and constraints passed to
+    the constructor.
+
+    See [Ament2023logei]_ for details. Formally,
+
+    `LogPF(x) = Sum_i log(P(y_i \in [lower_i, upper_i]))`,
+
+    where `y_i ~ constraint_i(x)` and `lower_i`, `upper_i` are the lower and
+    upper bounds for the i-th constraint, respectively.
+
+    Example:
+        # example where the 0th output has a non-negativity constraint
+        >>> model = SingleTaskGP(train_X, train_Y)
+        >>> constraints = {0: (0.0, None)}
+        >>> LogPOF = LogProbabilityOfFeasibility(model, constraints)
+        >>> cei = LogPF(test_X)
+    """
+
+    _log: bool = True
+
+    def __init__(
+        self,
+        model: Model,
+        constraints: dict[int, tuple[float | None, float | None]],
+    ) -> None:
+        r"""Analytic Log Probability of Feasibility.
+
+        Args:
+            model: A fitted multi-output model.
+            constraints: A dictionary of the form `{i: [lower, upper]}`, where
+                `i` is the output index, and `lower` and `upper` are lower and upper
+                bounds on that output (resp. interpreted as -Inf / Inf if None)
+        """
+        # Use AcquisitionFunction constructor to avoid check for posterior transform.
+        AcquisitionFunction.__init__(self, model=model)
+        self.posterior_transform = None
+        ConstrainedAnalyticAcquisitionFunctionMixin.__init__(self, constraints)
+        self.register_forward_pre_hook(convert_to_target_pre_hook)
+
+    @t_batch_mode_transform(expected_q=1)
+    def forward(self, X: Tensor) -> Tensor:
+        r"""Evaluate Constrained Log Probability of Feasibility on the candidate set X.
+
+        Args:
+            X: A `(b) x 1 x d`-dim Tensor of `(b)` t-batches of `d`-dim design
+                points each.
+
+        Returns:
+            A `(b)`-dim Tensor of Log Probability of Feasibility values at the given
+            design points `X`.
+        """
+        means, sigmas = self._mean_and_sigma(X)  # (b) x 1 + (m = num constraints)
+        return self._compute_log_prob_feas(means=means, sigmas=sigmas)
+
+
+class ConstrainedExpectedImprovement(
+    AnalyticAcquisitionFunction, ConstrainedAnalyticAcquisitionFunctionMixin
+):
     r"""Constrained Expected Improvement (feasibility-weighted).
 
     Computes the analytic expected improvement for a Normal posterior
@@ -543,13 +713,12 @@ def __init__(
         """
         legacy_ei_numerics_warning(legacy_name=type(self).__name__)
         # Use AcquisitionFunction constructor to avoid check for posterior transform.
-        super(AnalyticAcquisitionFunction, self).__init__(model=model)
+        AcquisitionFunction.__init__(self, model=model)
         self.posterior_transform = None
         self.maximize = maximize
         self.objective_index = objective_index
-        self.constraints = constraints
         self.register_buffer("best_f", torch.as_tensor(best_f))
-        _preprocess_constraint_bounds(self, constraints=constraints)
+        ConstrainedAnalyticAcquisitionFunctionMixin.__init__(self, constraints)
         self.register_forward_pre_hook(convert_to_target_pre_hook)
 
     @t_batch_mode_transform(expected_q=1)
@@ -569,7 +738,7 @@ def forward(self, X: Tensor) -> Tensor:
         mean_obj, sigma_obj = means[..., ind], sigmas[..., ind]
         u = _scaled_improvement(mean_obj, sigma_obj, self.best_f, self.maximize)
         ei = sigma_obj * _ei_helper(u)
-        log_prob_feas = _compute_log_prob_feas(self, means=means, sigmas=sigmas)
+        log_prob_feas = self._compute_log_prob_feas(means=means, sigmas=sigmas)
         return ei.mul(log_prob_feas.exp())
 
 
@@ -1131,82 +1300,3 @@ def _get_noiseless_fantasy_model(
     fantasy_model.likelihood.noise_covar.noise = Yvar
 
     return fantasy_model
-
-
-def _preprocess_constraint_bounds(
-    acqf: LogConstrainedExpectedImprovement | ConstrainedExpectedImprovement,
-    constraints: dict[int, tuple[float | None, float | None]],
-) -> None:
-    r"""Set up constraint bounds.
-
-    Args:
-        constraints: A dictionary of the form `{i: [lower, upper]}`, where
-            `i` is the output index, and `lower` and `upper` are lower and upper
-            bounds on that output (resp. interpreted as -Inf / Inf if None)
-    """
-    con_lower, con_lower_inds = [], []
-    con_upper, con_upper_inds = [], []
-    con_both, con_both_inds = [], []
-    con_indices = list(constraints.keys())
-    if len(con_indices) == 0:
-        raise ValueError("There must be at least one constraint.")
-    if acqf.objective_index in con_indices:
-        raise ValueError(
-            "Output corresponding to objective should not be a constraint."
-        )
-    for k in con_indices:
-        if constraints[k][0] is not None and constraints[k][1] is not None:
-            if constraints[k][1] <= constraints[k][0]:
-                raise ValueError("Upper bound is less than the lower bound.")
-            con_both_inds.append(k)
-            con_both.append([constraints[k][0], constraints[k][1]])
-        elif constraints[k][0] is not None:
-            con_lower_inds.append(k)
-            con_lower.append(constraints[k][0])
-        elif constraints[k][1] is not None:
-            con_upper_inds.append(k)
-            con_upper.append(constraints[k][1])
-    # tensor-based indexing is much faster than list-based advanced indexing
-    for name, indices in [
-        ("con_lower_inds", con_lower_inds),
-        ("con_upper_inds", con_upper_inds),
-        ("con_both_inds", con_both_inds),
-        ("con_both", con_both),
-        ("con_lower", con_lower),
-        ("con_upper", con_upper),
-    ]:
-        acqf.register_buffer(name, tensor=torch.as_tensor(indices))
-
-
-def _compute_log_prob_feas(
-    acqf: LogConstrainedExpectedImprovement | ConstrainedExpectedImprovement,
-    means: Tensor,
-    sigmas: Tensor,
-) -> Tensor:
-    r"""Compute logarithm of the feasibility probability for each batch of X.
-
-    Args:
-        X: A `(b) x 1 x d`-dim Tensor of `(b)` t-batches of `d`-dim design
-            points each.
-        means: A `(b) x m`-dim Tensor of means.
-        sigmas: A `(b) x m`-dim Tensor of standard deviations.
-    Returns:
-        A `b`-dim tensor of log feasibility probabilities
-
-    Note: This function does case-work for upper bound, lower bound, and both-sided
-    bounds. Another way to do it would be to use 'inf' and -'inf' for the
-    one-sided bounds and use the logic for the both-sided case. But this
-    causes an issue with autograd since we get 0 * inf.
-    TODO: Investigate further.
-    """
-    acqf.to(device=means.device)
-    return compute_log_prob_feas_from_bounds(
-        acqf.con_lower_inds,
-        acqf.con_upper_inds,
-        acqf.con_both_inds,
-        acqf.con_lower,
-        acqf.con_upper,
-        acqf.con_both,
-        means,
-        sigmas,
-    )

botorch/acquisition/factory.py

@@ -145,6 +145,16 @@ def get_acquisition_function(
             constraints=constraints,
             eta=eta,
         )
+    elif acquisition_function_name == "qLogPF":
+        return logei.qLogProbabilityOfFeasibility(
+            model=model,
+            constraints=constraints,
+            sampler=sampler,
+            objective=objective,
+            posterior_transform=posterior_transform,
+            X_pending=X_pending,
+            eta=eta,
+        )
     elif acquisition_function_name in ["qNEI", "qLogNEI"]:
         acqf_class = (
             monte_carlo.qNoisyExpectedImprovement