# Source code for botorch.optim.optimize

```
#!/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"""
Methods for optimizing acquisition functions.
"""
from __future__ import annotations
from typing import Any, Callable, Dict, List, Optional, Tuple, Union
import torch
from botorch.acquisition.acquisition import (
AcquisitionFunction,
OneShotAcquisitionFunction,
)
from botorch.acquisition.knowledge_gradient import qKnowledgeGradient
from botorch.generation.gen import gen_candidates_scipy
from botorch.logging import logger
from botorch.optim.initializers import (
gen_batch_initial_conditions,
gen_one_shot_kg_initial_conditions,
)
from botorch.optim.stopping import ExpMAStoppingCriterion
from torch import Tensor
INIT_OPTION_KEYS = {
# set of options for initialization that we should
# not pass to scipy.optimize.minimize to avoid
# warnings
"alpha",
"batch_limit",
"eta",
"init_batch_limit",
"nonnegative",
"n_burnin",
"sample_around_best",
"sample_around_best_sigma",
"sample_around_best_prob_perturb",
"sample_around_best_prob_perturb",
"seed",
"thinning",
}
[docs]def optimize_acqf(
acq_function: AcquisitionFunction,
bounds: Tensor,
q: int,
num_restarts: int,
raw_samples: Optional[int] = None,
options: Optional[Dict[str, Union[bool, float, int, str]]] = None,
inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
equality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
nonlinear_inequality_constraints: Optional[List[Callable]] = None,
fixed_features: Optional[Dict[int, float]] = None,
post_processing_func: Optional[Callable[[Tensor], Tensor]] = None,
batch_initial_conditions: Optional[Tensor] = None,
return_best_only: bool = True,
sequential: bool = False,
**kwargs: Any,
) -> Tuple[Tensor, Tensor]:
r"""Generate a set of candidates via multi-start optimization.
Args:
acq_function: An AcquisitionFunction.
bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`.
q: The number of candidates.
num_restarts: The number of starting points for multistart acquisition
function optimization.
raw_samples: The number of samples for initialization. This is required
if `batch_initial_conditions` is not specified.
options: Options for candidate generation.
inequality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) >= rhs`
equality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) = rhs`
nonlinear_inequality_constraints: A list of callables with that represent
non-linear inequality constraints of the form `callable(x) >= 0`. Each
callable is expected to take a `(num_restarts) x q x d`-dim tensor as an
input and return a `(num_restarts) x q`-dim tensor with the constraint
values. The constraints will later be passed to SLSQP. You need to pass in
`batch_initial_conditions` in this case. Using non-linear inequality
constraints also requires that `batch_limit` is set to 1, which will be
done automatically if not specified in `options`.
fixed_features: A map `{feature_index: value}` for features that
should be fixed to a particular value during generation.
post_processing_func: A function that post-processes an optimization
result appropriately (i.e., according to `round-trip`
transformations).
batch_initial_conditions: A tensor to specify the initial conditions. Set
this if you do not want to use default initialization strategy.
return_best_only: If False, outputs the solutions corresponding to all
random restart initializations of the optimization.
sequential: If False, uses joint optimization, otherwise uses sequential
optimization.
kwargs: Additonal keyword arguments.
Returns:
A two-element tuple containing
- a `(num_restarts) x q x d`-dim tensor of generated candidates.
- a tensor of associated acquisition values. If `sequential=False`,
this is a `(num_restarts)`-dim tensor of joint acquisition values
(with explicit restart dimension if `return_best_only=False`). If
`sequential=True`, this is a `q`-dim tensor of expected acquisition
values conditional on having observed canidates `0,1,...,i-1`.
Example:
>>> # generate `q=2` candidates jointly using 20 random restarts
>>> # and 512 raw samples
>>> candidates, acq_value = optimize_acqf(qEI, bounds, 2, 20, 512)
>>> generate `q=3` candidates sequentially using 15 random restarts
>>> # and 256 raw samples
>>> qEI = qExpectedImprovement(model, best_f=0.2)
>>> bounds = torch.tensor([[0.], [1.]])
>>> candidates, acq_value_list = optimize_acqf(
>>> qEI, bounds, 3, 15, 256, sequential=True
>>> )
"""
if sequential and q > 1:
if not return_best_only:
raise NotImplementedError(
"`return_best_only=False` only supported for joint optimization."
)
if isinstance(acq_function, OneShotAcquisitionFunction):
raise NotImplementedError(
"sequential optimization currently not supported for one-shot "
"acquisition functions. Must have `sequential=False`."
)
candidate_list, acq_value_list = [], []
base_X_pending = acq_function.X_pending
for i in range(q):
candidate, acq_value = optimize_acqf(
acq_function=acq_function,
bounds=bounds,
q=1,
num_restarts=num_restarts,
raw_samples=raw_samples,
options=options or {},
inequality_constraints=inequality_constraints,
equality_constraints=equality_constraints,
nonlinear_inequality_constraints=nonlinear_inequality_constraints,
fixed_features=fixed_features,
post_processing_func=post_processing_func,
batch_initial_conditions=None,
return_best_only=True,
sequential=False,
)
candidate_list.append(candidate)
acq_value_list.append(acq_value)
candidates = torch.cat(candidate_list, dim=-2)
acq_function.set_X_pending(
torch.cat([base_X_pending, candidates], dim=-2)
if base_X_pending is not None
else candidates
)
logger.info(f"Generated sequential candidate {i+1} of {q}")
# Reset acq_func to previous X_pending state
acq_function.set_X_pending(base_X_pending)
return candidates, torch.stack(acq_value_list)
options = options or {}
# Handle the trivial case when all features are fixed
if fixed_features is not None and len(fixed_features) == bounds.shape[-1]:
X = torch.tensor(
[fixed_features[i] for i in range(bounds.shape[-1])],
device=bounds.device,
dtype=bounds.dtype,
)
X = X.expand(q, *X.shape)
with torch.no_grad():
acq_value = acq_function(X)
return X, acq_value
if batch_initial_conditions is None:
if nonlinear_inequality_constraints:
raise NotImplementedError(
"`batch_initial_conditions` must be given if there are non-linear "
"inequality constraints."
)
if raw_samples is None:
raise ValueError(
"Must specify `raw_samples` when `batch_initial_conditions` is `None`."
)
ic_gen = (
gen_one_shot_kg_initial_conditions
if isinstance(acq_function, qKnowledgeGradient)
else gen_batch_initial_conditions
)
batch_initial_conditions = ic_gen(
acq_function=acq_function,
bounds=bounds,
q=q,
num_restarts=num_restarts,
raw_samples=raw_samples,
fixed_features=fixed_features,
options=options,
inequality_constraints=inequality_constraints,
equality_constraints=equality_constraints,
)
batch_limit: int = options.get(
"batch_limit", num_restarts if not nonlinear_inequality_constraints else 1
)
batch_candidates_list: List[Tensor] = []
batch_acq_values_list: List[Tensor] = []
batched_ics = batch_initial_conditions.split(batch_limit)
for i, batched_ics_ in enumerate(batched_ics):
# optimize using random restart optimization
batch_candidates_curr, batch_acq_values_curr = gen_candidates_scipy(
initial_conditions=batched_ics_,
acquisition_function=acq_function,
lower_bounds=bounds[0],
upper_bounds=bounds[1],
options={k: v for k, v in options.items() if k not in INIT_OPTION_KEYS},
inequality_constraints=inequality_constraints,
equality_constraints=equality_constraints,
nonlinear_inequality_constraints=nonlinear_inequality_constraints,
fixed_features=fixed_features,
)
batch_candidates_list.append(batch_candidates_curr)
batch_acq_values_list.append(batch_acq_values_curr)
logger.info(f"Generated candidate batch {i+1} of {len(batched_ics)}.")
batch_candidates = torch.cat(batch_candidates_list)
batch_acq_values = torch.cat(batch_acq_values_list)
if post_processing_func is not None:
batch_candidates = post_processing_func(batch_candidates)
if return_best_only:
best = torch.argmax(batch_acq_values.view(-1), dim=0)
batch_candidates = batch_candidates[best]
batch_acq_values = batch_acq_values[best]
if isinstance(acq_function, OneShotAcquisitionFunction):
if not kwargs.get("return_full_tree", False):
batch_candidates = acq_function.extract_candidates(X_full=batch_candidates)
return batch_candidates, batch_acq_values
[docs]def optimize_acqf_cyclic(
acq_function: AcquisitionFunction,
bounds: Tensor,
q: int,
num_restarts: int,
raw_samples: Optional[int] = None,
options: Optional[Dict[str, Union[bool, float, int, str]]] = None,
inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
equality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
fixed_features: Optional[Dict[int, float]] = None,
post_processing_func: Optional[Callable[[Tensor], Tensor]] = None,
batch_initial_conditions: Optional[Tensor] = None,
cyclic_options: Optional[Dict[str, Union[bool, float, int, str]]] = None,
) -> Tuple[Tensor, Tensor]:
r"""Generate a set of `q` candidates via cyclic optimization.
Args:
acq_function: An AcquisitionFunction
bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`.
q: The number of candidates.
num_restarts: Number of starting points for multistart acquisition
function optimization.
raw_samples: Number of samples for initialization. This is required
if `batch_initial_conditions` is not specified.
options: Options for candidate generation.
inequality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) >= rhs`
equality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) = rhs`
fixed_features: A map `{feature_index: value}` for features that
should be fixed to a particular value during generation.
post_processing_func: A function that post-processes an optimization
result appropriately (i.e., according to `round-trip`
transformations).
batch_initial_conditions: A tensor to specify the initial conditions.
If no initial conditions are provided, the default initialization will
be used.
cyclic_options: Options for stopping criterion for outer cyclic optimization.
Returns:
A two-element tuple containing
- a `q x d`-dim tensor of generated candidates.
- a `q`-dim tensor of expected acquisition values, where the value at
index `i` is the acquisition value conditional on having observed
all candidates except candidate `i`.
Example:
>>> # generate `q=3` candidates cyclically using 15 random restarts
>>> # 256 raw samples, and 4 cycles
>>>
>>> qEI = qExpectedImprovement(model, best_f=0.2)
>>> bounds = torch.tensor([[0.], [1.]])
>>> candidates, acq_value_list = optimize_acqf_cyclic(
>>> qEI, bounds, 3, 15, 256, cyclic_options={"maxiter": 4}
>>> )
"""
# for the first cycle, optimize the q candidates sequentially
candidates, acq_vals = optimize_acqf(
acq_function=acq_function,
bounds=bounds,
q=q,
num_restarts=num_restarts,
raw_samples=raw_samples,
options=options,
inequality_constraints=inequality_constraints,
equality_constraints=equality_constraints,
fixed_features=fixed_features,
post_processing_func=post_processing_func,
batch_initial_conditions=batch_initial_conditions,
return_best_only=True,
sequential=True,
)
if q > 1:
cyclic_options = cyclic_options or {}
stopping_criterion = ExpMAStoppingCriterion(**cyclic_options)
stop = stopping_criterion.evaluate(fvals=acq_vals)
base_X_pending = acq_function.X_pending
idxr = torch.ones(q, dtype=torch.bool, device=bounds.device)
while not stop:
for i in range(q):
# optimize only candidate i
idxr[i] = 0
acq_function.set_X_pending(
torch.cat([base_X_pending, candidates[idxr]], dim=-2)
if base_X_pending is not None
else candidates[idxr]
)
candidate_i, acq_val_i = optimize_acqf(
acq_function=acq_function,
bounds=bounds,
q=1,
num_restarts=num_restarts,
raw_samples=raw_samples,
options=options,
inequality_constraints=inequality_constraints,
equality_constraints=equality_constraints,
fixed_features=fixed_features,
post_processing_func=post_processing_func,
batch_initial_conditions=candidates[i].unsqueeze(0),
return_best_only=True,
sequential=True,
)
candidates[i] = candidate_i
acq_vals[i] = acq_val_i
idxr[i] = 1
stop = stopping_criterion.evaluate(fvals=acq_vals)
acq_function.set_X_pending(base_X_pending)
return candidates, acq_vals
[docs]def optimize_acqf_list(
acq_function_list: List[AcquisitionFunction],
bounds: Tensor,
num_restarts: int,
raw_samples: Optional[int] = None,
options: Optional[Dict[str, Union[bool, float, int, str]]] = None,
inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
equality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
fixed_features: Optional[Dict[int, float]] = None,
post_processing_func: Optional[Callable[[Tensor], Tensor]] = None,
) -> Tuple[Tensor, Tensor]:
r"""Generate a list of candidates from a list of acquisition functions.
The acquisition functions are optimized in sequence, with previous candidates
set as `X_pending`. This is also known as sequential greedy optimization.
Args:
acq_function_list: A list of acquisition functions.
bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`.
num_restarts: Number of starting points for multistart acquisition
function optimization.
raw_samples: Number of samples for initialization. This is required
if `batch_initial_conditions` is not specified.
options: Options for candidate generation.
inequality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) >= rhs`
equality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) = rhs`
fixed_features: A map `{feature_index: value}` for features that
should be fixed to a particular value during generation.
post_processing_func: A function that post-processes an optimization
result appropriately (i.e., according to `round-trip`
transformations).
Returns:
A two-element tuple containing
- a `q x d`-dim tensor of generated candidates.
- a `q`-dim tensor of expected acquisition values, where the value at
index `i` is the acquisition value conditional on having observed
all candidates except candidate `i`.
"""
if not acq_function_list:
raise ValueError("acq_function_list must be non-empty.")
candidate_list, acq_value_list = [], []
candidates = torch.tensor([], device=bounds.device, dtype=bounds.dtype)
base_X_pending = acq_function_list[0].X_pending
for acq_function in acq_function_list:
if candidate_list:
acq_function.set_X_pending(
torch.cat([base_X_pending, candidates], dim=-2)
if base_X_pending is not None
else candidates
)
candidate, acq_value = optimize_acqf(
acq_function=acq_function,
bounds=bounds,
q=1,
num_restarts=num_restarts,
raw_samples=raw_samples,
options=options or {},
inequality_constraints=inequality_constraints,
equality_constraints=equality_constraints,
fixed_features=fixed_features,
post_processing_func=post_processing_func,
return_best_only=True,
sequential=False,
)
candidate_list.append(candidate)
acq_value_list.append(acq_value)
candidates = torch.cat(candidate_list, dim=-2)
return candidates, torch.stack(acq_value_list)
[docs]def optimize_acqf_mixed(
acq_function: AcquisitionFunction,
bounds: Tensor,
q: int,
num_restarts: int,
fixed_features_list: List[Dict[int, float]],
raw_samples: Optional[int] = None,
options: Optional[Dict[str, Union[bool, float, int, str]]] = None,
inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
equality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
post_processing_func: Optional[Callable[[Tensor], Tensor]] = None,
batch_initial_conditions: Optional[Tensor] = None,
**kwargs: Any,
) -> Tuple[Tensor, Tensor]:
r"""Optimize over a list of fixed_features and returns the best solution.
This is useful for optimizing over mixed continuous and discrete domains.
For q > 1 this function always performs sequential greedy optimization (with
proper conditioning on generated candidates).
Args:
acq_function: An AcquisitionFunction
bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`.
q: The number of candidates.
num_restarts: Number of starting points for multistart acquisition
function optimization.
raw_samples: Number of samples for initialization. This is required
if `batch_initial_conditions` is not specified.
fixed_features_list: A list of maps `{feature_index: value}`. The i-th
item represents the fixed_feature for the i-th optimization.
options: Options for candidate generation.
inequality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) >= rhs`
equality constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) = rhs`
post_processing_func: A function that post-processes an optimization
result appropriately (i.e., according to `round-trip`
transformations).
batch_initial_conditions: A tensor to specify the initial conditions. Set
this if you do not want to use default initialization strategy.
Returns:
A two-element tuple containing
- a `q x d`-dim tensor of generated candidates.
- an associated acquisition value.
"""
if not fixed_features_list:
raise ValueError("fixed_features_list must be non-empty.")
if q == 1:
ff_candidate_list, ff_acq_value_list = [], []
for fixed_features in fixed_features_list:
candidate, acq_value = optimize_acqf(
acq_function=acq_function,
bounds=bounds,
q=q,
num_restarts=num_restarts,
raw_samples=raw_samples,
options=options or {},
inequality_constraints=inequality_constraints,
equality_constraints=equality_constraints,
fixed_features=fixed_features,
post_processing_func=post_processing_func,
batch_initial_conditions=batch_initial_conditions,
return_best_only=True,
)
ff_candidate_list.append(candidate)
ff_acq_value_list.append(acq_value)
ff_acq_values = torch.stack(ff_acq_value_list)
best = torch.argmax(ff_acq_values)
return ff_candidate_list[best], ff_acq_values[best]
# For batch optimization with q > 1 we do not want to enumerate all n_combos^n
# possible combinations of discrete choices. Instead, we use sequential greedy
# optimization.
base_X_pending = acq_function.X_pending
candidates = torch.tensor([], device=bounds.device, dtype=bounds.dtype)
for _ in range(q):
candidate, acq_value = optimize_acqf_mixed(
acq_function=acq_function,
bounds=bounds,
q=1,
num_restarts=num_restarts,
raw_samples=raw_samples,
fixed_features_list=fixed_features_list,
options=options or {},
inequality_constraints=inequality_constraints,
equality_constraints=equality_constraints,
post_processing_func=post_processing_func,
batch_initial_conditions=batch_initial_conditions,
)
candidates = torch.cat([candidates, candidate], dim=-2)
acq_function.set_X_pending(
torch.cat([base_X_pending, candidates], dim=-2)
if base_X_pending is not None
else candidates
)
acq_function.set_X_pending(base_X_pending)
acq_value = acq_function(candidates) # compute joint acquisition value
return candidates, acq_value
[docs]def optimize_acqf_discrete(
acq_function: AcquisitionFunction,
q: int,
choices: Tensor,
max_batch_size: int = 2048,
unique: bool = True,
**kwargs: Any,
) -> Tuple[Tensor, Tensor]:
r"""Optimize over a discrete set of points using batch evaluation.
For `q > 1` this function generates candidates by means of sequential
conditioning (rather than joint optimization), since for all but the
smalles number of choices the set `choices^q` of discrete points to
evaluate quickly explodes.
Args:
acq_function: An AcquisitionFunction.
q: The number of candidates.
choices: A `num_choices x d` tensor of possible choices.
max_batch_size: The maximum number of choices to evaluate in batch.
A large limit can cause excessive memory usage if the model has
a large training set.
unique: If True return unique choices, o/w choices may be repeated
(only relevant if `q > 1`).
Returns:
A three-element tuple containing
- a `q x d`-dim tensor of generated candidates.
- an associated acquisition value.
"""
choices_batched = choices.unsqueeze(-2)
if q > 1:
candidate_list, acq_value_list = [], []
base_X_pending = acq_function.X_pending
for _ in range(q):
with torch.no_grad():
acq_values = _split_batch_eval_acqf(
acq_function=acq_function,
X=choices_batched,
max_batch_size=max_batch_size,
)
best_idx = torch.argmax(acq_values)
candidate_list.append(choices_batched[best_idx])
acq_value_list.append(acq_values[best_idx])
# set pending points
candidates = torch.cat(candidate_list, dim=-2)
acq_function.set_X_pending(
torch.cat([base_X_pending, candidates], dim=-2)
if base_X_pending is not None
else candidates
)
# need to remove choice from choice set if enforcing uniqueness
if unique:
choices_batched = torch.cat(
[choices_batched[:best_idx], choices_batched[best_idx + 1 :]]
)
# Reset acq_func to previous X_pending state
acq_function.set_X_pending(base_X_pending)
return candidates, torch.stack(acq_value_list)
with torch.no_grad():
acq_values = _split_batch_eval_acqf(
acq_function=acq_function, X=choices_batched, max_batch_size=max_batch_size
)
best_idx = torch.argmax(acq_values)
return choices_batched[best_idx], acq_values[best_idx]
def _split_batch_eval_acqf(
acq_function: AcquisitionFunction, X: Tensor, max_batch_size: int
) -> Tensor:
return torch.cat([acq_function(X_) for X_ in X.split(max_batch_size)])
def _generate_neighbors(
x: Tensor,
discrete_choices: List[Tensor],
X_avoid: Tensor,
inequality_constraints: List[Tuple[Tensor, Tensor, float]],
):
# generate all 1D perturbations
npts = sum([len(c) for c in discrete_choices])
X_loc = x.repeat(npts, 1)
j = 0
for i, c in enumerate(discrete_choices):
X_loc[j : j + len(c), i] = c
j += len(c)
# remove invalid and infeasible points (also remove x)
X_loc = _filter_invalid(X=X_loc, X_avoid=torch.cat((X_avoid, x)))
X_loc = _filter_infeasible(X=X_loc, inequality_constraints=inequality_constraints)
return X_loc
def _filter_infeasible(
X: Tensor, inequality_constraints: List[Tuple[Tensor, Tensor, float]]
):
"""Remove all points from `X` that don't satisfy the constraints."""
is_feasible = torch.ones(X.shape[0], dtype=torch.bool, device=X.device)
for (inds, weights, bound) in inequality_constraints:
is_feasible &= (X[..., inds] * weights).sum(dim=-1) >= bound
return X[is_feasible]
def _filter_invalid(X: Tensor, X_avoid: Tensor):
"""Remove all occurences of `X_avoid` from `X`."""
return X[~(X == X_avoid.unsqueeze(-2)).all(dim=-1).any(dim=-2)]
def _gen_batch_initial_conditions_local_search(
discrete_choices: List[Tensor],
raw_samples: int,
X_avoid: Tensor,
inequality_constraints: List[Tuple[Tensor, Tensor, float]],
min_points: int,
max_tries: int = 100,
):
"""Generate initial conditions for local search."""
tkwargs = {"device": discrete_choices[0].device, "dtype": discrete_choices[0].dtype}
dim = len(discrete_choices)
X = torch.zeros(0, dim, **tkwargs)
for _ in range(max_tries):
X_new = torch.zeros(raw_samples, dim, **tkwargs)
for i, c in enumerate(discrete_choices):
X_new[:, i] = c[
torch.randint(low=0, high=len(c), size=(raw_samples,), device=c.device)
]
X = torch.unique(torch.cat((X, X_new)), dim=0)
X = _filter_invalid(X=X, X_avoid=X_avoid)
X = _filter_infeasible(X=X, inequality_constraints=inequality_constraints)
if len(X) >= min_points:
return X
raise RuntimeError(f"Failed to generate at least {min_points} initial conditions")
[docs]def optimize_acqf_discrete_local_search(
acq_function: AcquisitionFunction,
discrete_choices: List[Tensor],
q: int,
num_restarts: int = 20,
raw_samples: int = 4096,
inequality_constraints: Optional[List[Tuple[Tensor, Tensor, float]]] = None,
X_avoid: Optional[Tensor] = None,
batch_initial_conditions: Optional[Tensor] = None,
max_batch_size: int = 2048,
unique: bool = True,
**kwargs: Any,
) -> Tuple[Tensor, Tensor]:
r"""Optimize acquisition function over a lattice.
This is useful when d is large and enumeration of the search space
isn't possible. For q > 1 this function always performs sequential
greedy optimization (with proper conditioning on generated candidates).
NOTE: While this method supports arbitrary lattices, it has only been
thoroughly tested for {0, 1}^d. Consider it to be in alpha stage for
the more general case.
Args:
acq_function: An AcquisitionFunction
discrete_choices: A list of possible discrete choices for each dimension.
Each element in the list is expected to be a torch tensor.
q: The number of candidates.
num_restarts: Number of starting points for multistart acquisition
function optimization.
raw_samples: Number of samples for initialization. This is required
if `batch_initial_conditions` is not specified.
inequality_constraints: A list of tuples (indices, coefficients, rhs),
with each tuple encoding an inequality constraint of the form
`\sum_i (X[indices[i]] * coefficients[i]) >= rhs`
X_avoid: An `n x d` tensor of candidates that we aren't allowed to pick.
batch_initial_conditions: A tensor of size `n x 1 x d` to specify the
initial conditions. Set this if you do not want to use default
initialization strategy.
max_batch_size: The maximum number of choices to evaluate in batch.
A large limit can cause excessive memory usage if the model has
a large training set.
unique: If True return unique choices, o/w choices may be repeated
(only relevant if `q > 1`).
Returns:
A two-element tuple containing
- a `q x d`-dim tensor of generated candidates.
- an associated acquisition value.
"""
candidate_list = []
base_X_pending = acq_function.X_pending if q > 1 else None
base_X_avoid = X_avoid
tkwargs = {"device": discrete_choices[0].device, "dtype": discrete_choices[0].dtype}
dim = len(discrete_choices)
if X_avoid is None:
X_avoid = torch.zeros(0, dim, **tkwargs)
inequality_constraints = inequality_constraints or []
for i in range(q):
# generate some starting points
if i == 0 and batch_initial_conditions is not None:
X0 = _filter_invalid(X=batch_initial_conditions.squeeze(1), X_avoid=X_avoid)
X0 = _filter_infeasible(
X=X0, inequality_constraints=inequality_constraints
).unsqueeze(1)
else:
X_init = _gen_batch_initial_conditions_local_search(
discrete_choices=discrete_choices,
raw_samples=raw_samples,
X_avoid=X_avoid,
inequality_constraints=inequality_constraints,
min_points=num_restarts,
)
# pick the best starting points
with torch.no_grad():
acqvals_init = _split_batch_eval_acqf(
acq_function=acq_function,
X=X_init.unsqueeze(1),
max_batch_size=max_batch_size,
).unsqueeze(-1)
X0 = X_init[acqvals_init.topk(k=num_restarts, largest=True, dim=0).indices]
# optimize from the best starting points
best_xs = torch.zeros(len(X0), dim, **tkwargs)
best_acqvals = torch.zeros(len(X0), 1, **tkwargs)
for j, x in enumerate(X0):
curr_x, curr_acqval = x.clone(), acq_function(x.unsqueeze(1))
while True:
# this generates all feasible neighbors that are one bit away
X_loc = _generate_neighbors(
x=curr_x,
discrete_choices=discrete_choices,
X_avoid=X_avoid,
inequality_constraints=inequality_constraints,
)
# there may not be any neighbors
if len(X_loc) == 0:
break
with torch.no_grad():
acqval_loc = acq_function(X_loc.unsqueeze(1))
# break if no neighbor is better than the current point (local optimum)
if acqval_loc.max() <= curr_acqval:
break
best_ind = acqval_loc.argmax().item()
curr_x, curr_acqval = X_loc[best_ind].unsqueeze(0), acqval_loc[best_ind]
best_xs[j, :], best_acqvals[j] = curr_x, curr_acqval
# pick the best
best_idx = best_acqvals.argmax()
candidate_list.append(best_xs[best_idx].unsqueeze(0))
# set pending points
candidates = torch.cat(candidate_list, dim=-2)
if q > 1:
acq_function.set_X_pending(
torch.cat([base_X_pending, candidates], dim=-2)
if base_X_pending is not None
else candidates
)
# Update points to avoid if unique is True
if unique:
X_avoid = (
torch.cat([base_X_avoid, candidates], dim=-2)
if base_X_avoid is not None
else candidates
)
# Reset acq_func to original X_pending state
if q > 1:
acq_function.set_X_pending(base_X_pending)
with torch.no_grad():
acq_value = acq_function(candidates) # compute joint acquisition value
return candidates, acq_value
```