# Source code for botorch.utils.multi_objective.scalarization

```
#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# 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, UnsupportedError
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.
The augmented Chebyshev scalarization is given by
g(y) = max_i(w_i * y_i) + alpha * sum_i(w_i * y_i)
where the goal is to minimize g(y) in the setting where all objectives y_i are
to be minimized. Since the default in BoTorch is to maximize all objectives,
this method constructs a Chebyshev scalarization where the inputs are first
multiplied by -1, so that all objectives are to be minimized. Then, it computes
g(y) (which should be minimized), and returns -g(y), which should be maximized.
Minimizing an objective is supported by passing a negative
weight for that objective. To make all w * y's have the same sign
such that they are comparable when computing max(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]. If `n=0`, then outcomes
are left unnormalized.
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)
"""
# the chebyshev_obj assumes all objectives should be minimized, so
# multiply Y by -1
Y = -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.max(dim=-1).values + alpha * product.sum(dim=-1)
# A boolean mask indicating if minimizing an objective
minimize = weights < 0
if Y.shape[-2] == 0:
if minimize.any():
raise UnsupportedError(
"negative weights (for minimization) are only supported if "
"Y is provided."
)
# If there are no observations, we do not need to normalize the objectives
def obj(Y: Tensor, X: Optional[Tensor] = None) -> Tensor:
# multiply the scalarization by -1, so that the scalarization should
# be maximized
return -chebyshev_obj(Y=-Y)
return 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])
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
# multiply the scalarization by -1, so that the scalarization should
# be maximized
return -chebyshev_obj(Y=Y_normalized)
return obj
```