# Source code for botorch.utils.multi_objective.scalarization

#!/usr/bin/env python3
#
# LICENSE file in the root directory of this source tree.

r"""
Helper utilities for constructing scalarizations.

References

.. [Knowles2005]
J. Knowles, "ParEGO: a hybrid algorithm with on-line landscape approximation
for expensive multiobjective optimization problems," in IEEE Transactions
on Evolutionary Computation, vol. 10, no. 1, pp. 50-66, Feb. 2006.
"""
from __future__ import annotations

from typing import Callable, Optional

import torch
from botorch.exceptions.errors import BotorchTensorDimensionError
from botorch.utils.transforms import normalize
from torch import Tensor

[docs]def get_chebyshev_scalarization( weights: Tensor, Y: Tensor, alpha: float = 0.05 ) -> Callable[[Tensor, Optional[Tensor]], Tensor]: r"""Construct an augmented Chebyshev scalarization. Augmented Chebyshev scalarization: objective(y) = min(w * y) + alpha * sum(w * y) Outcomes are first normalized to [0,1] for maximization (or [-1,0] for minimization) and then an augmented Chebyshev scalarization is applied. Note: this assumes maximization of the augmented Chebyshev scalarization. Minimizing/Maximizing an objective is supported by passing a negative/positive weight for that objective. To make all w * y's have positive sign such that they are comparable when computing min(w * y), outcomes of minimization objectives are shifted from [0,1] to [-1,0]. See [Knowles2005]_ for details. This scalarization can be used with qExpectedImprovement to implement q-ParEGO as proposed in [Daulton2020qehvi]_. Args: weights: A m-dim tensor of weights. Positive for maximization and negative for minimization. Y: A n x m-dim tensor of observed outcomes, which are used for scaling the outcomes to [0,1] or [-1,0]. alpha: Parameter governing the influence of the weighted sum term. The default value comes from [Knowles2005]_. Returns: Transform function using the objective weights. Example: >>> weights = torch.tensor([0.75, -0.25]) >>> transform = get_aug_chebyshev_scalarization(weights, Y) """ if weights.shape != Y.shape[-1:]: raise BotorchTensorDimensionError( "weights must be an m-dim tensor where Y is ... x m." f"Got shapes {weights.shape} and {Y.shape}." ) elif Y.ndim > 2: raise NotImplementedError("Batched Y is not currently supported.") def chebyshev_obj(Y: Tensor, X: Optional[Tensor] = None) -> Tensor: product = weights * Y return product.min(dim=-1).values + alpha * product.sum(dim=-1) if Y.shape[-2] == 0: # If there are no observations, we do not need to normalize the objectives return chebyshev_obj if Y.shape[-2] == 1: # If there is only one observation, set the bounds to be # [min(Y_m), min(Y_m) + 1] for each objective m. This ensures we do not # divide by zero Y_bounds = torch.cat([Y, Y + 1], dim=0) else: # Set the bounds to be [min(Y_m), max(Y_m)], for each objective m Y_bounds = torch.stack([Y.min(dim=-2).values, Y.max(dim=-2).values]) # A boolean mask indicating if minimizing an objective minimize = weights < 0 def obj(Y: Tensor, X: Optional[Tensor] = None) -> Tensor: # scale to [0,1] Y_normalized = normalize(Y, bounds=Y_bounds) # If minimizing an objective, convert Y_normalized values to [-1,0], # such that min(w*y) makes sense, we want all w*y's to be positive Y_normalized[..., minimize] = Y_normalized[..., minimize] - 1 return chebyshev_obj(Y=Y_normalized) return obj