# Source code for botorch.acquisition.multi_objective.multi_fidelity

```
#!/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"""
Multi-Fidelity Acquisition Functions for Multi-objective Bayesian optimization.
References
.. [Irshad2021MOMF]
F. Irshad, S. Karsch, and A. Döpp. Expected hypervolume improvement for
simultaneous multi-objective and multi-fidelity optimization.
arXiv preprint arXiv:2112.13901, 2021.
"""
from __future__ import annotations
from typing import Callable, Optional, Union
import torch
from botorch.acquisition.cost_aware import InverseCostWeightedUtility
from botorch.acquisition.multi_objective.monte_carlo import (
qExpectedHypervolumeImprovement,
)
from botorch.acquisition.multi_objective.objective import MCMultiOutputObjective
from botorch.models.cost import AffineFidelityCostModel
from botorch.models.deterministic import GenericDeterministicModel
from botorch.models.model import Model
from botorch.sampling.base import MCSampler
from botorch.utils.multi_objective.box_decompositions.non_dominated import (
NondominatedPartitioning,
)
from botorch.utils.transforms import concatenate_pending_points, t_batch_mode_transform
from torch import Tensor
[docs]
class MOMF(qExpectedHypervolumeImprovement):
def __init__(
self,
model: Model,
ref_point: Union[list[float], Tensor],
partitioning: NondominatedPartitioning,
sampler: Optional[MCSampler] = None,
objective: Optional[MCMultiOutputObjective] = None,
constraints: Optional[list[Callable[[Tensor], Tensor]]] = None,
eta: Union[Tensor, float] = 1e-3,
X_pending: Optional[Tensor] = None,
cost_call: Optional[Callable[[Tensor], Tensor]] = None,
) -> None:
r"""MOMF acquisition function supporting m>=2 outcomes.
The model needs to have train_obj that has a fidelity
objective appended to its end.
In the following example we consider a 2-D output space
but the ref_point is 3D because of fidelity objective.
See [Irshad2021MOMF]_ for details.
Example:
>>> model = SingleTaskGP(train_X, train_Y)
>>> ref_point = [0.0, 0.0, 0.0]
>>> cost_func = lambda X: 5 + X[..., -1]
>>> momf = MOMF(model, ref_point, partitioning, cost_func)
>>> momf_val = momf(test_X)
Args:
model: A fitted model. There are two default assumptions in the training
data. `train_X` should have fidelity parameter `s` as the last dimension
of the input and `train_Y` contains a trust objective as its last
dimension.
ref_point: A list or tensor with `m+1` elements representing the reference
point (in the outcome space) w.r.t. to which compute the hypervolume.
The '+1' takes care of the trust objective appended to `train_Y`.
This is a reference point for the objective values (i.e. after
applying`objective` to the samples).
partitioning: A `NondominatedPartitioning` module that provides the non-
dominated front and a partitioning of the non-dominated space in hyper-
rectangles. If constraints are present, this partitioning must only
include feasible points.
sampler: The sampler used to draw base samples. If not given,
a sampler is generated using `get_sampler`.
objective: The MCMultiOutputObjective under which the samples are evaluated.
Defaults to `IdentityMCMultiOutputObjective()`.
constraints: A list of callables, each mapping a Tensor of dimension
`sample_shape x batch-shape x q x m` to a Tensor of dimension
`sample_shape x batch-shape x q`, where negative values imply
feasibility. The acquisition function will compute expected feasible
hypervolume.
X_pending: A `batch_shape x m x d`-dim Tensor of `m` design points that have
points that have been submitted for function evaluation but have not yet
been evaluated. Concatenated into `X` upon forward call. Copied and set
to have no gradient.
cost_call: A callable cost function mapping a Tensor of dimension
`batch_shape x q x d` to a cost Tensor of dimension
`batch_shape x q x m`. Defaults to an AffineCostModel with
`C(s) = 1 + s`.
eta: The temperature parameter for the sigmoid function used for the
differentiable approximation of the constraints. In case of a float the
same eta is used for every constraint in constraints. In case of a
tensor the length of the tensor must match the number of provided
constraints. The i-th constraint is then estimated with the i-th
eta value.
"""
if len(ref_point) != partitioning.num_outcomes:
raise ValueError(
"The length of the reference point must match the number of outcomes. "
f"Got ref_point with {len(ref_point)} elements, but expected "
f"{partitioning.num_outcomes}."
)
ref_point = torch.as_tensor(
ref_point,
dtype=partitioning.pareto_Y.dtype,
device=partitioning.pareto_Y.device,
)
super().__init__(
model=model,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
objective=objective,
constraints=constraints,
eta=eta,
X_pending=X_pending,
)
if cost_call is None:
cost_model = AffineFidelityCostModel(
fidelity_weights={-1: 1.0}, fixed_cost=1.0
)
else:
cost_model = GenericDeterministicModel(cost_call)
cost_aware_utility = InverseCostWeightedUtility(cost_model=cost_model)
self.cost_aware_utility = cost_aware_utility
[docs]
@concatenate_pending_points
@t_batch_mode_transform()
def forward(self, X: Tensor) -> Tensor:
posterior = self.model.posterior(X)
samples = self.get_posterior_samples(posterior)
hv_gain = self._compute_qehvi(samples=samples, X=X)
cost_weighted_qehvi = self.cost_aware_utility(X=X, deltas=hv_gain)
return cost_weighted_qehvi
```