# Source code for botorch.acquisition.utils

```
#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
r"""
Utilities for acquisition functions.
"""
from __future__ import annotations
import math
import warnings
from typing import Callable, Dict, List, Optional
import torch
from botorch import settings
from botorch.acquisition import analytic, multi_objective
from botorch.acquisition import monte_carlo # noqa F401
from botorch.acquisition.acquisition import AcquisitionFunction
from botorch.acquisition.multi_objective import monte_carlo as moo_monte_carlo
from botorch.acquisition.objective import (
IdentityMCObjective,
MCAcquisitionObjective,
)
from botorch.exceptions.errors import UnsupportedError
from botorch.exceptions.warnings import SamplingWarning
from botorch.models.model import Model
from botorch.sampling.samplers import IIDNormalSampler, MCSampler, SobolQMCNormalSampler
from botorch.utils.multi_objective.box_decompositions.non_dominated import (
FastNondominatedPartitioning,
NondominatedPartitioning,
)
from torch import Tensor
from torch.quasirandom import SobolEngine
[docs]def get_acquisition_function(
acquisition_function_name: str,
model: Model,
objective: MCAcquisitionObjective,
X_observed: Tensor,
X_pending: Optional[Tensor] = None,
constraints: Optional[List[Callable[[Tensor], Tensor]]] = None,
mc_samples: int = 500,
qmc: bool = True,
seed: Optional[int] = None,
**kwargs,
) -> monte_carlo.MCAcquisitionFunction:
r"""Convenience function for initializing botorch acquisition functions.
Args:
acquisition_function_name: Name of the acquisition function.
model: A fitted model.
objective: A MCAcquisitionObjective.
X_observed: A `m1 x d`-dim Tensor of `m1` design points that have
already been observed.
X_pending: A `m2 x d`-dim Tensor of `m2` design points whose evaluation
is pending.
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. Used when constraint_transforms are not passed
as part of the objective.
mc_samples: The number of samples to use for (q)MC evaluation of the
acquisition function.
qmc: If True, use quasi-Monte-Carlo sampling (instead of iid).
seed: If provided, perform deterministic optimization (i.e. the
function to optimize is fixed and not stochastic).
Returns:
The requested acquisition function.
Example:
>>> model = SingleTaskGP(train_X, train_Y)
>>> obj = LinearMCObjective(weights=torch.tensor([1.0, 2.0]))
>>> acqf = get_acquisition_function("qEI", model, obj, train_X)
"""
# initialize the sampler
if qmc:
sampler = SobolQMCNormalSampler(num_samples=mc_samples, seed=seed)
else:
sampler = IIDNormalSampler(num_samples=mc_samples, seed=seed)
# instantiate and return the requested acquisition function
if acquisition_function_name in ("qEI", "qPI"):
obj = objective(model.posterior(X_observed).mean)
best_f = obj.max(dim=-1).values
if acquisition_function_name == "qEI":
return monte_carlo.qExpectedImprovement(
model=model,
best_f=best_f,
sampler=sampler,
objective=objective,
X_pending=X_pending,
)
elif acquisition_function_name == "qPI":
return monte_carlo.qProbabilityOfImprovement(
model=model,
best_f=best_f,
sampler=sampler,
objective=objective,
X_pending=X_pending,
tau=kwargs.get("tau", 1e-3),
)
elif acquisition_function_name == "qNEI":
return monte_carlo.qNoisyExpectedImprovement(
model=model,
X_baseline=X_observed,
sampler=sampler,
objective=objective,
X_pending=X_pending,
prune_baseline=kwargs.get("prune_baseline", False),
marginalize_dim=kwargs.get("marginalize_dim"),
)
elif acquisition_function_name == "qSR":
return monte_carlo.qSimpleRegret(
model=model, sampler=sampler, objective=objective, X_pending=X_pending
)
elif acquisition_function_name == "qUCB":
if "beta" not in kwargs:
raise ValueError("`beta` must be specified in kwargs for qUCB.")
return monte_carlo.qUpperConfidenceBound(
model=model,
beta=kwargs["beta"],
sampler=sampler,
objective=objective,
X_pending=X_pending,
)
elif acquisition_function_name == "qEHVI":
# pyre-fixme [16]: `Model` has no attribute `train_targets`
try:
ref_point = kwargs["ref_point"]
except KeyError:
raise ValueError("`ref_point` must be specified in kwargs for qEHVI")
try:
Y = kwargs["Y"]
except KeyError:
raise ValueError("`Y` must be specified in kwargs for qEHVI")
# get feasible points
if constraints is not None:
feas = torch.stack([c(Y) <= 0 for c in constraints], dim=-1).all(dim=-1)
Y = Y[feas]
obj = objective(Y)
alpha = kwargs.get("alpha", 0.0)
if alpha > 0:
partitioning = NondominatedPartitioning(
ref_point=torch.as_tensor(ref_point, dtype=Y.dtype, device=Y.device),
Y=obj,
alpha=alpha,
)
else:
partitioning = FastNondominatedPartitioning(
ref_point=torch.as_tensor(ref_point, dtype=Y.dtype, device=Y.device),
Y=obj,
)
return moo_monte_carlo.qExpectedHypervolumeImprovement(
model=model,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
objective=objective,
constraints=constraints,
X_pending=X_pending,
)
elif acquisition_function_name == "qNEHVI":
if "ref_point" not in kwargs:
raise ValueError("`ref_point` must be specified in kwargs for qNEHVI")
return moo_monte_carlo.qNoisyExpectedHypervolumeImprovement(
model=model,
ref_point=kwargs["ref_point"],
X_baseline=X_observed,
sampler=sampler,
objective=objective,
constraints=constraints,
prune_baseline=True,
alpha=kwargs.get("alpha", 0.0),
X_pending=X_pending,
marginalize_dim=kwargs.get("marginalize_dim"),
)
raise NotImplementedError(
f"Unknown acquisition function {acquisition_function_name}"
)
[docs]def get_infeasible_cost(
X: Tensor,
model: Model,
objective: Optional[Callable[[Tensor, Optional[Tensor]], Tensor]] = None,
) -> float:
r"""Get infeasible cost for a model and objective.
Computes an infeasible cost `M` such that `-M < min_x f(x)` almost always,
so that feasible points are preferred.
Args:
X: A `n x d` Tensor of `n` design points to use in evaluating the
minimum. These points should cover the design space well. The more
points the better the estimate, at the expense of added computation.
model: A fitted botorch model.
objective: The objective with which to evaluate the model output.
Returns:
The infeasible cost `M` value.
Example:
>>> model = SingleTaskGP(train_X, train_Y)
>>> objective = lambda Y: Y[..., -1] ** 2
>>> M = get_infeasible_cost(train_X, model, obj)
"""
if objective is None:
def objective(Y: Tensor, X: Optional[Tensor] = None):
return Y.squeeze(-1)
posterior = model.posterior(X)
lb = objective(posterior.mean - 6 * posterior.variance.clamp_min(0).sqrt()).min()
M = -(lb.clamp_max(0.0))
return M.item()
[docs]def is_nonnegative(acq_function: AcquisitionFunction) -> bool:
r"""Determine whether a given acquisition function is non-negative.
Args:
acq_function: The `AcquisitionFunction` instance.
Returns:
True if `acq_function` is non-negative, False if not, or if the behavior
is unknown (for custom acquisition functions).
Example:
>>> qEI = qExpectedImprovement(model, best_f=0.1)
>>> is_nonnegative(qEI) # returns True
"""
return isinstance(
acq_function,
(
analytic.ExpectedImprovement,
analytic.ConstrainedExpectedImprovement,
analytic.ProbabilityOfImprovement,
analytic.NoisyExpectedImprovement,
monte_carlo.qExpectedImprovement,
monte_carlo.qNoisyExpectedImprovement,
monte_carlo.qProbabilityOfImprovement,
multi_objective.analytic.ExpectedHypervolumeImprovement,
multi_objective.monte_carlo.qExpectedHypervolumeImprovement,
multi_objective.monte_carlo.qNoisyExpectedHypervolumeImprovement,
),
)
[docs]def prune_inferior_points(
model: Model,
X: Tensor,
objective: Optional[MCAcquisitionObjective] = None,
num_samples: int = 2048,
max_frac: float = 1.0,
sampler: Optional[MCSampler] = None,
marginalize_dim: Optional[int] = None,
) -> Tensor:
r"""Prune points from an input tensor that are unlikely to be the best point.
Given a model, an objective, and an input tensor `X`, this function returns
the subset of points in `X` that have some probability of being the best
point under the objective. This function uses sampling to estimate the
probabilities, the higher the number of points `n` in `X` the higher the
number of samples `num_samples` should be to obtain accurate estimates.
Args:
model: A fitted model. Batched models are currently not supported.
X: An input tensor of shape `n x d`. Batched inputs are currently not
supported.
objective: The objective under which to evaluate the posterior.
num_samples: The number of samples used to compute empirical
probabilities of being the best point.
max_frac: The maximum fraction of points to retain. Must satisfy
`0 < max_frac <= 1`. Ensures that the number of elements in the
returned tensor does not exceed `ceil(max_frac * n)`.
sampler: If provided, will use this customized sampler instead of
automatically constructing one with `num_samples`.
marginalize_dim: A batch dimension that should be marginalized.
For example, this is useful when using a batched fully Bayesian
model.
Returns:
A `n' x d` with subset of points in `X`, where
n' = min(N_nz, ceil(max_frac * n))
with `N_nz` the number of points in `X` that have non-zero (empirical,
under `num_samples` samples) probability of being the best point.
"""
if X.ndim > 2:
# TODO: support batched inputs (req. dealing with ragged tensors)
raise UnsupportedError(
"Batched inputs `X` are currently unsupported by prune_inferior_points"
)
max_points = math.ceil(max_frac * X.size(-2))
if max_points < 1 or max_points > X.size(-2):
raise ValueError(f"max_frac must take values in (0, 1], is {max_frac}")
with torch.no_grad():
posterior = model.posterior(X=X)
if sampler is None:
if posterior.base_sample_shape.numel() > SobolEngine.MAXDIM:
if settings.debug.on():
warnings.warn(
f"Sample dimension q*m={posterior.base_sample_shape.numel()} "
f"exceeding Sobol max dimension ({SobolEngine.MAXDIM}). "
"Using iid samples instead.",
SamplingWarning,
)
sampler = IIDNormalSampler(num_samples=num_samples)
else:
sampler = SobolQMCNormalSampler(num_samples=num_samples)
samples = sampler(posterior)
if objective is None:
objective = IdentityMCObjective()
obj_vals = objective(samples, X=X)
if obj_vals.ndim > 2:
if obj_vals.ndim == 3 and marginalize_dim is not None:
obj_vals = obj_vals.mean(dim=marginalize_dim)
else:
# TODO: support batched inputs (req. dealing with ragged tensors)
raise UnsupportedError(
"Models with multiple batch dims are currently unsupported by"
" prune_inferior_points."
)
is_best = torch.argmax(obj_vals, dim=-1)
idcs, counts = torch.unique(is_best, return_counts=True)
if len(idcs) > max_points:
counts, order_idcs = torch.sort(counts, descending=True)
idcs = order_idcs[:max_points]
return X[idcs]
[docs]def project_to_target_fidelity(
X: Tensor, target_fidelities: Optional[Dict[int, float]] = None
) -> Tensor:
r"""Project `X` onto the target set of fidelities.
This function assumes that the set of feasible fidelities is a box, so
projecting here just means setting each fidelity parameter to its target
value.
Args:
X: A `batch_shape x q x d`-dim Tensor of with `q` `d`-dim design points
for each t-batch.
target_fidelities: A dictionary mapping a subset of columns of `X` (the
fidelity parameters) to their respective target fidelity value. If
omitted, assumes that the last column of X is the fidelity parameter
with a target value of 1.0.
Return:
A `batch_shape x q x d`-dim Tensor `X_proj` with fidelity parameters
projected to the provided fidelity values.
"""
if target_fidelities is None:
target_fidelities = {-1: 1.0}
d = X.size(-1)
# normalize to positive indices
tfs = {k if k >= 0 else d + k: v for k, v in target_fidelities.items()}
ones = torch.ones(*X.shape[:-1], device=X.device, dtype=X.dtype)
# here we're looping through the feature dimension of X - this could be
# slow for large `d`, we should optimize this for that case
X_proj = torch.stack(
[X[..., i] if i not in tfs else tfs[i] * ones for i in range(d)], dim=-1
)
return X_proj
[docs]def expand_trace_observations(
X: Tensor, fidelity_dims: Optional[List[int]] = None, num_trace_obs: int = 0
) -> Tensor:
r"""Expand `X` with trace observations.
Expand a tensor of inputs with "trace observations" that are obtained during
the evaluation of the candidate set. This is used in multi-fidelity
optimization. It can be though of as augmenting the `q`-batch with additional
points that are the expected trace observations.
Let `f_i` be the `i`-th fidelity parameter. Then this functions assumes that
for each element of the q-batch, besides the fidelity `f_i`, we will observe
additonal fidelities `f_i1, ..., f_iK`, where `K = num_trace_obs`, during
evaluation of the candidate set `X`. Specifically, this function assumes
that `f_ij = (K-j) / (num_trace_obs + 1) * f_i` for all `i`. That is, the
expansion is performed in parallel for all fidelities (it does not expand
out all possible combinations).
Args:
X: A `batch_shape x q x d`-dim Tensor of with `q` `d`-dim design points
(incl. the fidelity parameters) for each t-batch.
fidelity_dims: The indices of the fidelity parameters. If omitted,
assumes that the last column of X contains the fidelity parameters.
num_trace_obs: The number of trace observations to use.
Return:
A `batch_shape x (q + num_trace_obs x q) x d` Tensor `X_expanded` that
expands `X` with trace observations.
"""
if num_trace_obs == 0: # No need to expand if we don't use trace observations
return X
if fidelity_dims is None:
fidelity_dims = [-1]
# The general strategy in the following is to expand `X` to the desired
# shape, and then multiply it (point-wise) with a tensor of scaling factors
reps = [1] * (X.ndim - 2) + [1 + num_trace_obs, 1]
X_expanded = X.repeat(*reps) # batch_shape x (q + num_trace_obs x q) x d
scale_fac = torch.ones_like(X_expanded)
s_pad = 1 / (num_trace_obs + 1)
# tensor of num_trace_obs scaling factors equally space between 1-s_pad and s_pad
sf = torch.linspace(1 - s_pad, s_pad, num_trace_obs, device=X.device, dtype=X.dtype)
# repeat each element q times
q = X.size(-2)
sf = torch.repeat_interleave(sf, q) # num_trace_obs * q
# now expand this to num_trace_obs x q x num_fidelities
sf = sf.unsqueeze(-1).expand(X_expanded.size(-2) - q, len(fidelity_dims))
# change relevant entries of the scaling tensor
scale_fac[..., q:, fidelity_dims] = sf
return scale_fac * X_expanded
[docs]def project_to_sample_points(X: Tensor, sample_points: Tensor) -> Tensor:
r"""Augment `X` with sample points at which to take weighted average.
Args:
X: A `batch_shape x 1 x d`-dim Tensor of with one d`-dim design points
for each t-batch.
sample_points: `p x d'`-dim Tensor (`d' < d`) of `d'`-dim sample points at
which to compute the expectation. The `d'`-dims refer to the trailing
columns of X.
Returns:
A `batch_shape x p x d` Tensor where the q-batch includes the `p` sample points.
"""
batch_shape = X.shape[:-2]
p, d_prime = sample_points.shape
X_new = X.repeat(*(1 for _ in batch_shape), p, 1) # batch_shape x p x d
X_new[..., -d_prime:] = sample_points
return X_new
```