Support different noise levels for different outputs in test functions (#2136)

Summary:
Adds support for different noise levels for different objectives in a multiobjective test function

Closes #2135

Modifies `BaseTestProblem` class to allow for `noise_std` to be a list of floats, where the length should be the number of objectives in a `MultiObjectiveTestProblem`. This way each component of the objective function can be subject to a separate noise level.

Pull Request resolved: #2136

Reviewed By: sdaulton

Differential Revision: D51791486

Pulled By: Balandat

fbshipit-source-id: 234fd2f2a97ac62f6f2913ac163fe4950a784891

Author: seanohagan

botorch/test_functions/base.py

@@ -11,9 +11,10 @@
 from __future__ import annotations
 
 from abc import ABC, abstractmethod
-from typing import List, Optional, Tuple
+from typing import List, Tuple, Union
 
 import torch
+
 from botorch.exceptions.errors import InputDataError
 from torch import Tensor
 from torch.nn import Module
@@ -26,11 +27,17 @@ class BaseTestProblem(Module, ABC):
     _bounds: List[Tuple[float, float]]
     _check_grad_at_opt: bool = True
 
-    def __init__(self, noise_std: Optional[float] = None, negate: bool = False) -> None:
+    def __init__(
+        self,
+        noise_std: Union[None, float, List[float]] = None,
+        negate: bool = False,
+    ) -> None:
         r"""Base constructor for test functions.
 
         Args:
-            noise_std: Standard deviation of the observation noise.
+            noise_std: Standard deviation of the observation noise. If a list is
+                provided, specifies separate noise standard deviations for each
+                objective in a multiobjective problem.
             negate: If True, negate the function.
         """
         super().__init__()
@@ -60,7 +67,8 @@ def forward(self, X: Tensor, noise: bool = True) -> Tensor:
         X = X if batch else X.unsqueeze(0)
         f = self.evaluate_true(X=X)
         if noise and self.noise_std is not None:
-            f += self.noise_std * torch.randn_like(f)
+            _noise = torch.tensor(self.noise_std, device=X.device, dtype=X.dtype)
+            f += _noise * torch.randn_like(f)
         if self.negate:
             f = -f
         return f if batch else f.squeeze(0)
@@ -82,6 +90,7 @@ class ConstrainedBaseTestProblem(BaseTestProblem, ABC):
 
     num_constraints: int
     _check_grad_at_opt: bool = False
+    constraint_noise_std: Union[None, float, List[float]] = None
 
     def evaluate_slack(self, X: Tensor, noise: bool = True) -> Tensor:
         r"""Evaluate the constraint slack on a set of points.
@@ -101,10 +110,11 @@ def evaluate_slack(self, X: Tensor, noise: bool = True) -> Tensor:
                 corresponds to the constraint being feasible).
         """
         cons = self.evaluate_slack_true(X=X)
-        if noise and self.noise_std is not None:
-            # TODO: Allow different noise levels for objective and constraints (and
-            # different noise levels between different constraints)
-            cons += self.noise_std * torch.randn_like(cons)
+        if noise and self.constraint_noise_std is not None:
+            _constraint_noise = torch.tensor(
+                self.constraint_noise_std, device=X.device, dtype=X.dtype
+            )
+            cons += _constraint_noise * torch.randn_like(cons)
         return cons
 
     def is_feasible(self, X: Tensor, noise: bool = True) -> Tensor:
@@ -147,13 +157,24 @@ class MultiObjectiveTestProblem(BaseTestProblem):
     _ref_point: List[float]
     _max_hv: float
 
-    def __init__(self, noise_std: Optional[float] = None, negate: bool = False) -> None:
+    def __init__(
+        self,
+        noise_std: Union[None, float, List[float]] = None,
+        negate: bool = False,
+    ) -> None:
         r"""Base constructor for multi-objective test functions.
 
         Args:
-            noise_std: Standard deviation of the observation noise.
+            noise_std: Standard deviation of the observation noise. If a list is
+                provided, specifies separate noise standard deviations for each
+                objective.
             negate: If True, negate the objectives.
         """
+        if isinstance(noise_std, list) and len(noise_std) != len(self._ref_point):
+            raise InputDataError(
+                f"If specified as a list, length of noise_std ({len(noise_std)}) "
+                f"must match the number of objectives ({len(self._ref_point)})"
+            )
         super().__init__(noise_std=noise_std, negate=negate)
         ref_point = torch.tensor(self._ref_point, dtype=torch.float)
         if negate:

botorch/test_functions/multi_objective.py

@@ -76,7 +76,7 @@
 import math
 from abc import ABC, abstractmethod
 from math import pi
-from typing import Optional
+from typing import List, Union
 
 import torch
 from botorch.exceptions.errors import UnsupportedError
@@ -116,7 +116,11 @@ class BraninCurrin(MultiObjectiveTestProblem):
     _ref_point = [18.0, 6.0]
     _max_hv = 59.36011874867746  # this is approximated using NSGA-II
 
-    def __init__(self, noise_std: Optional[float] = None, negate: bool = False) -> None:
+    def __init__(
+        self,
+        noise_std: Union[None, float, List[float]] = None,
+        negate: bool = False,
+    ) -> None:
         r"""
         Args:
             noise_std: Standard deviation of the observation noise.
@@ -174,7 +178,7 @@ class DH(MultiObjectiveTestProblem, ABC):
     def __init__(
         self,
         dim: int,
-        noise_std: Optional[float] = None,
+        noise_std: Union[None, float, List[float]] = None,
         negate: bool = False,
     ) -> None:
         r"""
@@ -334,7 +338,7 @@ def __init__(
         self,
         dim: int,
         num_objectives: int = 2,
-        noise_std: Optional[float] = None,
+        noise_std: Union[None, float, List[float]] = None,
         negate: bool = False,
     ) -> None:
         r"""
@@ -600,7 +604,7 @@ class GMM(MultiObjectiveTestProblem):
 
     def __init__(
         self,
-        noise_std: Optional[float] = None,
+        noise_std: Union[None, float, List[float]] = None,
         negate: bool = False,
         num_objectives: int = 2,
     ) -> None:
@@ -926,7 +930,7 @@ def __init__(
         self,
         dim: int,
         num_objectives: int = 2,
-        noise_std: Optional[float] = None,
+        noise_std: Union[None, float, List[float]] = None,
         negate: bool = False,
     ) -> None:
         r"""
@@ -1234,7 +1238,11 @@ class ConstrainedBraninCurrin(BraninCurrin, ConstrainedBaseTestProblem):
     _ref_point = [80.0, 12.0]
     _max_hv = 608.4004237022673  # from NSGA-II with 90k evaluations
 
-    def __init__(self, noise_std: Optional[float] = None, negate: bool = False) -> None:
+    def __init__(
+        self,
+        noise_std: Union[None, float, List[float]] = None,
+        negate: bool = False,
+    ) -> None:
         r"""
         Args:
             noise_std: Standard deviation of the observation noise.
@@ -1337,7 +1345,7 @@ class MW7(MultiObjectiveTestProblem, ConstrainedBaseTestProblem):
     def __init__(
         self,
         dim: int,
-        noise_std: Optional[float] = None,
+        noise_std: Union[None, float, List[float]] = None,
         negate: bool = False,
     ) -> None:
         r"""

botorch/test_functions/synthetic.py

@@ -47,9 +47,10 @@
 from __future__ import annotations
 
 import math
-from typing import List, Optional, Tuple
+from typing import List, Optional, Tuple, Union
 
 import torch
+from botorch.exceptions.errors import InputDataError
 from botorch.test_functions.base import BaseTestProblem, ConstrainedBaseTestProblem
 from botorch.test_functions.utils import round_nearest
 from torch import Tensor
@@ -64,13 +65,15 @@ class SyntheticTestFunction(BaseTestProblem):
 
     def __init__(
         self,
-        noise_std: Optional[float] = None,
+        noise_std: Union[None, float, List[float]] = None,
         negate: bool = False,
         bounds: Optional[List[Tuple[float, float]]] = None,
     ) -> None:
         r"""
         Args:
-            noise_std: Standard deviation of the observation noise.
+            noise_std: Standard deviation of the observation noise. If a list is
+                provided, specifies separate noise standard deviations for each
+                objective in a multiobjective problem.
             negate: If True, negate the function.
             bounds: Custom bounds for the function specified as (lower, upper) pairs.
         """
@@ -802,7 +805,61 @@ def evaluate_true(self, X: Tensor) -> Tensor:
 #  ------------ Constrained synthetic test functions ----------- #
 
 
-class ConstrainedGramacy(ConstrainedBaseTestProblem, SyntheticTestFunction):
+class ConstrainedSyntheticTestFunction(
+    ConstrainedBaseTestProblem, SyntheticTestFunction
+):
+    r"""Base class for constrained synthetic test functions."""
+
+    def __init__(
+        self,
+        noise_std: Union[None, float, List[float]] = None,
+        constraint_noise_std: Union[None, float, List[float]] = None,
+        negate: bool = False,
+        bounds: Optional[List[Tuple[float, float]]] = None,
+    ) -> None:
+        r"""
+        Args:
+            noise_std: Standard deviation of the observation noise. If a list is
+                provided, specifies separate noise standard deviations for each
+                objective in a multiobjective problem.
+            constraint_noise_std: Standard deviation of the constraint noise.
+                If a list is provided, specifies separate noise standard
+                deviations for each constraint.
+            negate: If True, negate the function.
+            bounds: Custom bounds for the function specified as (lower, upper) pairs.
+        """
+        self.constraint_noise_std = self._validate_constraint_noise(
+            constraint_noise_std
+        )
+        SyntheticTestFunction.__init__(
+            self, noise_std=noise_std, negate=negate, bounds=bounds
+        )
+
+    def _validate_constraint_noise(
+        self, constraint_noise_std
+    ) -> Union[None, float, List[float]]:
+        """
+        Validates that constraint_noise_std has length equal to
+        the number of constraints, if given as a list
+
+        Args:
+            constraint_noise_std: Standard deviation of the constraint noise.
+                If a list is provided, specifies separate noise standard
+                deviations for each constraint.
+        """
+        if (
+            isinstance(constraint_noise_std, list)
+            and len(constraint_noise_std) != self.num_constraints
+        ):
+            raise InputDataError(
+                "If specified as a list, length of constraint_noise_std "
+                f"({len(constraint_noise_std)}) must match the "
+                f"number of constraints ({self.num_constraints})"
+            )
+        return constraint_noise_std
+
+
+class ConstrainedGramacy(ConstrainedSyntheticTestFunction):
     r"""Constrained Gramacy test function.
 
     This problem comes from [Gramacy2016]_. The problem is defined
@@ -835,31 +892,77 @@ def evaluate_slack_true(self, X: Tensor) -> Tensor:
         return torch.cat([-c1, -c2], dim=-1)
 
 
-class ConstrainedHartmann(Hartmann, ConstrainedBaseTestProblem):
+class ConstrainedHartmann(Hartmann, ConstrainedSyntheticTestFunction):
     r"""Constrained Hartmann test function.
 
     This is a constrained version of the standard Hartmann test function that
     uses `||x||_2 <= 1` as the constraint. This problem comes from [Letham2019]_.
     """
     num_constraints = 1
 
+    def __init__(
+        self,
+        dim: int = 6,
+        noise_std: Union[None, float] = None,
+        constraint_noise_std: Union[None, float, List[float]] = None,
+        negate: bool = False,
+        bounds: Optional[List[Tuple[float, float]]] = None,
+    ) -> None:
+        r"""
+        Args:
+            dim: The (input) dimension.
+            noise_std: Standard deviation of the observation noise.
+            constraint_noise_std: Standard deviation of the constraint noise.
+                If a list is provided, specifies separate noise standard
+                deviations for each constraint.
+            negate: If True, negate the function.
+            bounds: Custom bounds for the function specified as (lower, upper) pairs.
+        """
+        self._validate_constraint_noise(constraint_noise_std)
+        Hartmann.__init__(
+            self, dim=dim, noise_std=noise_std, negate=negate, bounds=bounds
+        )
+
     def evaluate_slack_true(self, X: Tensor) -> Tensor:
         return -X.norm(dim=-1, keepdim=True) + 1
 
 
-class ConstrainedHartmannSmooth(Hartmann, ConstrainedBaseTestProblem):
+class ConstrainedHartmannSmooth(Hartmann, ConstrainedSyntheticTestFunction):
     r"""Smooth constrained Hartmann test function.
 
     This is a constrained version of the standard Hartmann test function that
     uses `||x||_2^2 <= 1` as the constraint to obtain smoother constraint slack.
     """
     num_constraints = 1
 
+    def __init__(
+        self,
+        dim: int = 6,
+        noise_std: Union[None, float] = None,
+        constraint_noise_std: Union[None, float, List[float]] = None,
+        negate: bool = False,
+        bounds: Optional[List[Tuple[float, float]]] = None,
+    ) -> None:
+        r"""
+        Args:
+            dim: The (input) dimension.
+            noise_std: Standard deviation of the observation noise.
+            constraint_noise_std: Standard deviation of the constraint noise.
+                If a list is provided, specifies separate noise standard
+                deviations for each constraint.
+            negate: If True, negate the function.
+            bounds: Custom bounds for the function specified as (lower, upper) pairs.
+        """
+        self._validate_constraint_noise(constraint_noise_std)
+        Hartmann.__init__(
+            self, dim=dim, noise_std=noise_std, negate=negate, bounds=bounds
+        )
+
     def evaluate_slack_true(self, X: Tensor) -> Tensor:
         return -X.pow(2).sum(dim=-1, keepdim=True) + 1
 
 
-class PressureVessel(SyntheticTestFunction, ConstrainedBaseTestProblem):
+class PressureVessel(ConstrainedSyntheticTestFunction):
     r"""Pressure vessel design problem with constraints.
 
     The four-dimensional pressure vessel design problem with four black-box
@@ -894,7 +997,7 @@ def evaluate_slack_true(self, X: Tensor) -> Tensor:
         )
 
 
-class WeldedBeamSO(SyntheticTestFunction, ConstrainedBaseTestProblem):
+class WeldedBeamSO(ConstrainedSyntheticTestFunction):
     r"""Welded beam design problem with constraints (single-outcome).
 
     The four-dimensional welded beam design proble problem with six
@@ -950,7 +1053,7 @@ def evaluate_slack_true(self, X: Tensor) -> Tensor:
         return -torch.stack([g1, g2, g3, g4, g5, g6], dim=-1)
 
 
-class TensionCompressionString(SyntheticTestFunction, ConstrainedBaseTestProblem):
+class TensionCompressionString(ConstrainedSyntheticTestFunction):
     r"""Tension compression string optimization problem with constraints.
 
     The three-dimensional tension compression string optimization problem with
@@ -981,7 +1084,7 @@ def evaluate_slack_true(self, X: Tensor) -> Tensor:
         return -constraints.clamp_max(100)
 
 
-class SpeedReducer(SyntheticTestFunction, ConstrainedBaseTestProblem):
+class SpeedReducer(ConstrainedSyntheticTestFunction):
     r"""Speed Reducer design problem with constraints.
 
     The seven-dimensional speed reducer design problem with eleven black-box