#!/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"""
Monte-Carlo Acquisition Functions for Multi-objective Bayesian optimization.
References
.. [Daulton2020qehvi]
S. Daulton, M. Balandat, and E. Bakshy. Differentiable Expected Hypervolume
Improvement for Parallel Multi-Objective Bayesian Optimization. Advances in Neural
Information Processing Systems 33, 2020.
.. [Daulton2021nehvi]
S. Daulton, M. Balandat, and E. Bakshy. Parallel Bayesian Optimization of
Multiple Noisy Objectives. ArXiv, 2021.
"""
from __future__ import annotations
import warnings
from abc import abstractmethod
from copy import deepcopy
from itertools import combinations
from typing import Any, Callable, List, Optional, Union
import torch
from botorch.acquisition.acquisition import AcquisitionFunction
from botorch.acquisition.multi_objective.objective import (
IdentityMCMultiOutputObjective,
MCMultiOutputObjective,
)
from botorch.acquisition.multi_objective.utils import (
prune_inferior_points_multi_objective,
)
from botorch.exceptions.errors import UnsupportedError
from botorch.exceptions.warnings import BotorchWarning
from botorch.models.model import Model
from botorch.posteriors.posterior import Posterior
from botorch.sampling.samplers import MCSampler, SobolQMCNormalSampler
from botorch.utils.multi_objective.box_decompositions.box_decomposition_list import (
BoxDecompositionList,
)
from botorch.utils.multi_objective.box_decompositions.dominated import (
DominatedPartitioning,
)
from botorch.utils.multi_objective.box_decompositions.non_dominated import (
FastNondominatedPartitioning,
NondominatedPartitioning,
)
from botorch.utils.multi_objective.box_decompositions.utils import (
_pad_batch_pareto_frontier,
)
from botorch.utils.objective import apply_constraints_nonnegative_soft
from botorch.utils.torch import BufferDict
from botorch.utils.transforms import (
concatenate_pending_points,
match_batch_shape,
t_batch_mode_transform,
)
from torch import Tensor
[docs]class MultiObjectiveMCAcquisitionFunction(AcquisitionFunction):
r"""Abstract base class for Multi-Objective batch acquisition functions."""
def __init__(
self,
model: Model,
sampler: Optional[MCSampler] = None,
objective: Optional[MCMultiOutputObjective] = None,
X_pending: Optional[Tensor] = None,
) -> None:
r"""Constructor for the MCAcquisitionFunction base class.
Args:
model: A fitted model.
sampler: The sampler used to draw base samples. Defaults to
`SobolQMCNormalSampler(num_samples=128, collapse_batch_dims=True)`.
objective: The MCMultiOutputObjective under which the samples are
evaluated. Defaults to `IdentityMultiOutputObjective()`.
X_pending: A `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.
"""
super().__init__(model=model)
if sampler is None:
sampler = SobolQMCNormalSampler(num_samples=128, collapse_batch_dims=True)
self.add_module("sampler", sampler)
if objective is None:
objective = IdentityMCMultiOutputObjective()
elif not isinstance(objective, MCMultiOutputObjective):
raise UnsupportedError(
"Only objectives of type MCMultiOutputObjective are supported for "
"Multi-Objective MC acquisition functions."
)
self.add_module("objective", objective)
self.X_pending = None
if X_pending is not None:
self.set_X_pending(X_pending)
[docs] @abstractmethod
def forward(self, X: Tensor) -> Tensor:
r"""Takes in a `batch_shape x q x d` X Tensor of t-batches with `q` `d`-dim
design points each, and returns a Tensor with shape `batch_shape'`, where
`batch_shape'` is the broadcasted batch shape of model and input `X`. Should
utilize the result of `set_X_pending` as needed to account for pending function
evaluations.
"""
pass # pragma: no cover
[docs]class qExpectedHypervolumeImprovement(MultiObjectiveMCAcquisitionFunction):
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,
X_pending: Optional[Tensor] = None,
eta: float = 1e-3,
) -> None:
r"""q-Expected Hypervolume Improvement supporting m>=2 outcomes.
See [Daulton2020qehvi]_ for details.
Example:
>>> model = SingleTaskGP(train_X, train_Y)
>>> ref_point = [0.0, 0.0]
>>> qEHVI = qExpectedHypervolumeImprovement(model, ref_point, partitioning)
>>> qehvi = qEHVI(test_X)
Args:
model: A fitted model.
ref_point: A list or tensor with `m` elements representing the reference
point (in the outcome space) w.r.t. to which compute the hypervolume.
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. Defaults to
`SobolQMCNormalSampler(num_samples=128, collapse_batch_dims=True)`.
objective: The MCMultiOutputObjective under which the samples are evaluated.
Defaults to `IdentityMultiOutputObjective()`.
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 acqusition 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.
eta: The temperature parameter for the sigmoid function used for the
differentiable approximation of the constraints.
"""
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, sampler=sampler, objective=objective, X_pending=X_pending
)
self.constraints = constraints
self.eta = eta
self.register_buffer("ref_point", ref_point)
cell_bounds = partitioning.get_hypercell_bounds()
self.register_buffer("cell_lower_bounds", cell_bounds[0])
self.register_buffer("cell_upper_bounds", cell_bounds[1])
self.q = -1
self.q_subset_indices = BufferDict()
def _cache_q_subset_indices(self, q: int) -> None:
r"""Cache indices corresponding to all subsets of `q`.
This means that consecutive calls to `forward` with the same
`q` will not recompute the indices for all (2^q - 1) subsets.
Note: this will use more memory than regenerating the indices
for each i and then deleting them, but it will be faster for
repeated evaluations (e.g. during optimization).
Args:
q: batch size
"""
if q != self.q:
indices = list(range(q))
tkwargs = {"dtype": torch.long, "device": self.cell_lower_bounds.device}
self.q_subset_indices = BufferDict(
{
f"q_choose_{i}": torch.tensor(
list(combinations(indices, i)), **tkwargs
)
for i in range(1, q + 1)
}
)
self.q = q
def _compute_qehvi(self, samples: Tensor, X: Optional[Tensor] = None) -> Tensor:
r"""Compute the expected (feasible) hypervolume improvement given MC samples.
Args:
samples: A `n_samples x batch_shape x q x m`-dim tensor of samples.
X: A `batch_shape x q x d`-dim tensor of inputs.
Returns:
A `batch_shape x (model_batch_shape)`-dim tensor of expected hypervolume
improvement for each batch.
"""
q = samples.shape[-2]
# Note that the objective may subset the outcomes (e.g. this will usually happen
# if there are constraints present).
obj = self.objective(samples, X=X)
if self.constraints is not None:
feas_weights = torch.ones(
obj.shape[:-1], device=obj.device, dtype=obj.dtype
)
feas_weights = apply_constraints_nonnegative_soft(
obj=feas_weights,
constraints=self.constraints,
samples=samples,
eta=self.eta,
)
self._cache_q_subset_indices(q=q)
batch_shape = samples.shape[:-2]
# this is n_samples x input_batch_shape x
areas_per_segment = torch.zeros(
*batch_shape,
self.cell_lower_bounds.shape[-2],
dtype=obj.dtype,
device=obj.device,
)
cell_batch_ndim = self.cell_lower_bounds.ndim - 2
sample_batch_view_shape = torch.Size(
[
batch_shape[0] if cell_batch_ndim > 0 else 1,
*[1 for _ in range(len(batch_shape) - max(cell_batch_ndim, 1))],
*self.cell_lower_bounds.shape[1:-2],
]
)
view_shape = (
*sample_batch_view_shape,
self.cell_upper_bounds.shape[-2],
1,
self.cell_upper_bounds.shape[-1],
)
for i in range(1, q + 1):
# TODO: we could use batches to compute (q choose i) and (q choose q-i)
# simulataneously since subsets of size i and q-i have the same number of
# elements. This would decrease the number of iterations, but increase
# memory usage.
q_choose_i = self.q_subset_indices[f"q_choose_{i}"]
# this tensor is mc_samples x batch_shape x i x q_choose_i x m
obj_subsets = obj.index_select(dim=-2, index=q_choose_i.view(-1))
obj_subsets = obj_subsets.view(
obj.shape[:-2] + q_choose_i.shape + obj.shape[-1:]
)
# since all hyperrectangles share one vertex, the opposite vertex of the
# overlap is given by the component-wise minimum.
# take the minimum in each subset
overlap_vertices = obj_subsets.min(dim=-2).values
# add batch-dim to compute area for each segment (pseudo-pareto-vertex)
# this tensor is mc_samples x batch_shape x num_cells x q_choose_i x m
overlap_vertices = torch.min(
overlap_vertices.unsqueeze(-3), self.cell_upper_bounds.view(view_shape)
)
# substract cell lower bounds, clamp min at zero
lengths_i = (
overlap_vertices - self.cell_lower_bounds.view(view_shape)
).clamp_min(0.0)
# take product over hyperrectangle side lengths to compute area
# sum over all subsets of size i
areas_i = lengths_i.prod(dim=-1)
# if constraints are present, apply a differentiable approximation of
# the indicator function
if self.constraints is not None:
feas_subsets = feas_weights.index_select(
dim=-1, index=q_choose_i.view(-1)
).view(feas_weights.shape[:-1] + q_choose_i.shape)
areas_i = areas_i * feas_subsets.unsqueeze(-3).prod(dim=-1)
areas_i = areas_i.sum(dim=-1)
# Using the inclusion-exclusion principle, set the sign to be positive
# for subsets of odd sizes and negative for subsets of even size
areas_per_segment += (-1) ** (i + 1) * areas_i
# sum over segments and average over MC samples
return areas_per_segment.sum(dim=-1).mean(dim=0)
[docs] @concatenate_pending_points
@t_batch_mode_transform()
def forward(self, X: Tensor) -> Tensor:
posterior = self.model.posterior(X)
samples = self.sampler(posterior)
return self._compute_qehvi(samples=samples)
[docs]class qNoisyExpectedHypervolumeImprovement(qExpectedHypervolumeImprovement):
def __init__(
self,
model: Model,
ref_point: Union[List[float], Tensor],
X_baseline: Tensor,
sampler: Optional[MCSampler] = None,
objective: Optional[MCMultiOutputObjective] = None,
constraints: Optional[List[Callable[[Tensor], Tensor]]] = None,
X_pending: Optional[Tensor] = None,
eta: float = 1e-3,
prune_baseline: bool = False,
alpha: float = 0.0,
cache_pending: bool = True,
max_iep: int = 0,
incremental_nehvi: bool = True,
**kwargs: Any,
) -> None:
r"""q-Noisy Expected Hypervolume Improvement supporting m>=2 outcomes.
See [Daulton2021nehvi]_ for details.
Example:
>>> model = SingleTaskGP(train_X, train_Y)
>>> ref_point = [0.0, 0.0]
>>> qNEHVI = qNoisyExpectedHypervolumeImprovement(model, ref_point, train_X)
>>> qnehvi = qNEHVI(test_X)
Args:
model: A fitted model.
ref_point: A list or tensor with `m` elements representing the reference
point (in the outcome space) w.r.t. to which compute the hypervolume.
This is a reference point for the objective values (i.e. after
applying `objective` to the samples).
X_baseline: A `r x d`-dim Tensor of `r` design points that have already
been observed. These points are considered as potential approximate
pareto-optimal design points.
sampler: The sampler used to draw base samples. Defaults to
`SobolQMCNormalSampler(num_samples=128, collapse_batch_dims=True)`.
Note: a pareto front is created for each mc sample, which can be
computationally intensive for `m` > 2.
objective: The MCMultiOutputObjective under which the samples are
evaluated. Defaults to `IdentityMultiOutputObjective()`.
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 acqusition 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.
eta: The temperature parameter for the sigmoid function used for the
differentiable approximation of the constraints.
prune_baseline: If True, remove points in `X_baseline` that are
highly unlikely to be the pareto optimal and better than the
reference point. This can significantly improve computation time and
is generally recommended. In order to customize pruning parameters,
instead manually call `prune_inferior_points_multi_objective` on
`X_baseline` before instantiating the acquisition function.
alpha: The hyperparameter controlling the approximate non-dominated
partitioning. The default value of 0.0 means an exact partitioning
is used. As the number of objectives `m` increases, consider increasing
this parameter in order to limit computational complexity.
cache_pending: A boolean indicating whether to use cached box
decompositions (CBD) for handling pending points. This is
generally recommended.
max_iep: The maximum number of pending points before the box
decompositions will be recomputed.
incremental_nehvi: A boolean indicating whether to compute the
incremental NEHVI from the `i`th point where `i=1, ..., q`
under sequential greedy optimization, or the full qNEHVI over
`q` points.
"""
ref_point = torch.as_tensor(
ref_point, dtype=X_baseline.dtype, device=X_baseline.device
)
super(qExpectedHypervolumeImprovement, self).__init__(
model=model, sampler=sampler, objective=objective
)
if not self.sampler.collapse_batch_dims:
raise UnsupportedError(
"qNoisyExpectedHypervolumeImprovement currently requires sampler "
"to use `collapse_batch_dims=True`."
)
elif self.sampler.base_samples is not None:
warnings.warn(
message=(
"sampler.base_samples is not None. qNEHVI requires that the "
"base_samples be initialized to None. Resetting "
"sampler.base_samples to None."
),
category=BotorchWarning,
)
self.sampler.base_samples = None
if X_baseline.ndim > 2:
raise UnsupportedError(
"qNoisyExpectedHypervolumeImprovement does not support batched "
f"X_baseline. Expected 2 dims, got {X_baseline.ndim}."
)
if prune_baseline:
X_baseline = prune_inferior_points_multi_objective(
model=model,
X=X_baseline,
objective=objective,
constraints=constraints,
ref_point=ref_point,
marginalize_dim=kwargs.get("marginalize_dim"),
)
self.register_buffer("ref_point", ref_point)
self.base_sampler = deepcopy(self.sampler)
self.constraints = constraints
self.alpha = alpha
self.eta = eta
self.q = -1
self.q_subset_indices = BufferDict()
self.partitioning = None
# set partitioning class and args
self.p_kwargs = {}
if self.alpha > 0:
self.p_kwargs["alpha"] = self.alpha
self.p_class = NondominatedPartitioning
else:
self.p_class = FastNondominatedPartitioning
self.register_buffer("_X_baseline", X_baseline)
self.register_buffer("_X_baseline_and_pending", X_baseline)
self.register_buffer(
"cache_pending",
torch.tensor(cache_pending, dtype=bool),
)
self.register_buffer(
"_prev_nehvi",
torch.tensor(0.0, dtype=ref_point.dtype, device=ref_point.device),
)
self.register_buffer(
"_max_iep",
torch.tensor(max_iep, dtype=torch.long),
)
self.register_buffer(
"incremental_nehvi",
torch.tensor(incremental_nehvi, dtype=torch.bool),
)
if X_pending is not None:
# this will call self._set_cell_bounds if the number of pending
# points is greater than self._max_iep
self.set_X_pending(X_pending)
# In the case that X_pending is not None, but there are fewer than
# max_iep pending points, the box decompoisitions are not performed in
# set_X_pending. Therefore, we need to perform a box decomposition over
# f(X_baseline) here.
if X_pending is None or X_pending.shape[-2] <= self._max_iep:
self._set_cell_bounds(num_new_points=X_baseline.shape[0])
@property
def X_baseline(self) -> Tensor:
r"""Return X_baseline augmented with pending points cached using CBD."""
return self._X_baseline_and_pending
def _compute_initial_hvs(self, obj: Tensor, feas: Optional[Tensor] = None) -> None:
r"""Compute hypervolume dominated by f(X_baseline) under each sample.
Args:
obj: A `sample_shape x batch_shape x n x m`-dim tensor of samples
of objectives.
feas: `sample_shape x batch_shape x n`-dim tensor of samples
of feasiblity indicators.
"""
initial_hvs = []
for i, sample in enumerate(obj):
if self.constraints is not None:
sample = sample[feas[i]]
dominated_partitioning = DominatedPartitioning(
ref_point=self.ref_point,
Y=sample,
)
hv = dominated_partitioning.compute_hypervolume()
initial_hvs.append(hv)
self.register_buffer(
"_initial_hvs",
torch.tensor(initial_hvs, dtype=obj.dtype, device=obj.device).view(
self._batch_sample_shape, *obj.shape[-2:]
),
)
def _set_cell_bounds(self, num_new_points: int) -> None:
r"""Compute the box decomposition under each posterior sample.
Args:
num_new_points: The number of new points (beyond the points
in X_baseline) that were used in the previous box decomposition.
In the first box decomposition, this should be the number of points
in X_baseline.
"""
feas = None
if self.X_baseline.shape[0] > 0:
with torch.no_grad():
posterior = self.model.posterior(self.X_baseline)
# reset sampler
self.q = -1
self._set_sampler(q=num_new_points, posterior=posterior)
# set base_sampler
self.base_sampler.register_buffer(
"base_samples", self.sampler.base_samples.detach().clone()
)
samples = self.base_sampler(posterior)
obj = self.objective(samples)
if self.constraints is not None:
feas = torch.stack(
[c(samples) <= 0 for c in self.constraints], dim=0
).all(dim=0)
else:
obj = torch.empty(
*self.sampler._sample_shape,
0,
self.ref_point.shape[-1],
dtype=self.ref_point.dtype,
device=self.ref_point.device,
)
self._batch_sample_shape = obj.shape[:-2]
# collapse batch dimensions
# use numel() rather than view(-1) to handle case of no baseline points
new_batch_shape = self._batch_sample_shape.numel()
obj = obj.view(new_batch_shape, *obj.shape[-2:])
if self.constraints is not None and feas is not None:
feas = feas.view(new_batch_shape, *feas.shape[-1:])
if self.partitioning is None and not self.incremental_nehvi:
self._compute_initial_hvs(obj=obj, feas=feas)
if self.ref_point.shape[-1] > 2:
# the partitioning algorithms run faster on the CPU
# due to advanced indexing
ref_point_cpu = self.ref_point.cpu()
obj_cpu = obj.cpu()
if self.constraints is not None and feas is not None:
feas_cpu = feas.cpu()
obj_cpu = [obj_cpu[i][feas_cpu[i]] for i in range(obj.shape[0])]
partitionings = []
for sample in obj_cpu:
partitioning = self.p_class(
ref_point=ref_point_cpu, Y=sample, **self.p_kwargs
)
partitionings.append(partitioning)
self.partitioning = BoxDecompositionList(*partitionings)
else:
# use batched partitioning
obj = _pad_batch_pareto_frontier(
Y=obj,
ref_point=self.ref_point.unsqueeze(0).expand(
obj.shape[0], self.ref_point.shape[-1]
),
feasibility_mask=feas,
)
self.partitioning = self.p_class(
ref_point=self.ref_point, Y=obj, **self.p_kwargs
)
cell_bounds = self.partitioning.get_hypercell_bounds().to(self.ref_point)
cell_bounds = cell_bounds.view(
2, *self._batch_sample_shape, *cell_bounds.shape[-2:]
)
self.register_buffer("cell_lower_bounds", cell_bounds[0])
self.register_buffer("cell_upper_bounds", cell_bounds[1])
[docs] def set_X_pending(self, X_pending: Optional[Tensor] = None) -> None:
r"""Informs the acquisition function about pending design points.
Args:
X_pending: `n x d` Tensor with `n` `d`-dim design points that have
been submitted for evaluation but have not yet been evaluated.
"""
if X_pending is None:
self.X_pending = None
else:
if X_pending.requires_grad:
warnings.warn(
"Pending points require a gradient but the acquisition function"
" will not provide a gradient to these points.",
BotorchWarning,
)
X_pending = X_pending.detach().clone()
if self.cache_pending:
X_baseline = torch.cat([self._X_baseline, X_pending], dim=-2)
# number of new points is the total number of points minus
# (the number of previously cached pending points plus the
# of number of baseline points)
num_new_points = X_baseline.shape[0] - self.X_baseline.shape[0]
if num_new_points > 0:
if num_new_points > self._max_iep:
# set the new baseline points to include pending points
self.register_buffer("_X_baseline_and_pending", X_baseline)
# recompute box decompositions
self._set_cell_bounds(num_new_points=num_new_points)
if not self.incremental_nehvi:
self._prev_nehvi = (
(self._hypervolumes - self._initial_hvs)
.clamp_min(0.0)
.mean()
)
# set to None so that pending points are not concatenated in
# forward
self.X_pending = None
# set q=-1 to so that self.sampler is updated at the next
# forward call
self.q = -1
else:
self.X_pending = X_pending[-num_new_points:]
else:
self.X_pending = X_pending
@property
def _hypervolumes(self) -> Tensor:
r"""Compute hypervolume over X_baseline under each posterior sample.
Returns:
A `n_samples`-dim tensor of hypervolumes.
"""
return self.partitioning.compute_hypervolume().view(self._batch_sample_shape)
def _set_sampler(
self,
q: int,
posterior: Posterior,
) -> None:
r"""Update the sampler to use the original base samples for X_baseline.
Args:
q: the batch size
posterior: the posterior
TODO: refactor some/all of this into the MCSampler.
"""
if self.q != q:
# create new base_samples
base_sample_shape = self.sampler._get_base_sample_shape(posterior=posterior)
self.sampler._construct_base_samples(
posterior=posterior, shape=base_sample_shape
)
if (
self.X_baseline.shape[0] > 0
and self.base_sampler.base_samples is not None
):
current_base_samples = self.base_sampler.base_samples.detach().clone()
view_shape = (
base_sample_shape[0:1]
+ torch.Size([1] * (len(base_sample_shape) - 3))
+ current_base_samples.shape[-2:]
)
expanded_shape = (
base_sample_shape[:-2] + current_base_samples.shape[-2:]
)
# Use stored base samples:
# Use all base_samples from the current sampler
# this includes the base_samples from the base_sampler
# and any base_samples for the new points in the sampler.
# For example, when using sequential greedy candidate generation
# then generate the new candidate point using last (-1) base_sample
# in sampler. This copies that base sample.
end_idx = current_base_samples.shape[-2]
self.sampler.base_samples[..., :end_idx, :] = current_base_samples.view(
view_shape
).expand(expanded_shape)
# update cached subset indices
# Note: this also stores self.q = q
self._cache_q_subset_indices(q=q)
[docs] @concatenate_pending_points
@t_batch_mode_transform()
def forward(self, X: Tensor) -> Tensor:
X_full = torch.cat([match_batch_shape(self.X_baseline, X), X], dim=-2)
# Note: it is important to compute the full posterior over `(X_baseline, X)``
# to ensure that we properly sample `f(X)` from the joint distribution `
# `f(X_baseline, X) ~ P(f | D)` given that we can already fixed the sampled
# function values for `f(X_baseline)`
posterior = self.model.posterior(X_full)
q = X.shape[-2]
self._set_sampler(q=q, posterior=posterior)
samples = self.sampler(posterior)[..., -q:, :]
# add previous nehvi from pending points
return self._compute_qehvi(samples=samples) + self._prev_nehvi
