Source code for optuna.samplers._tpe.sampler

import math
from typing import Any
from typing import Callable
from typing import Container
from typing import Dict
from typing import List
from typing import Optional
from typing import Sequence
from typing import Tuple
from typing import Union
import warnings

import numpy as np

from optuna._hypervolume import WFG
from optuna._hypervolume.hssp import _solve_hssp
from optuna.distributions import BaseDistribution
from optuna.exceptions import ExperimentalWarning
from optuna.logging import get_logger
from optuna.samplers._base import _CONSTRAINTS_KEY
from optuna.samplers._base import _process_constraints_after_trial
from optuna.samplers._base import BaseSampler
from optuna.samplers._random import RandomSampler
from optuna.samplers._tpe.parzen_estimator import _ParzenEstimator
from optuna.samplers._tpe.parzen_estimator import _ParzenEstimatorParameters
from optuna.search_space import IntersectionSearchSpace
from optuna.search_space.group_decomposed import _GroupDecomposedSearchSpace
from optuna.search_space.group_decomposed import _SearchSpaceGroup
from optuna.study import Study
from optuna.study._study_direction import StudyDirection
from optuna.trial import FrozenTrial
from optuna.trial import TrialState


EPS = 1e-12
_logger = get_logger(__name__)


def default_gamma(x: int) -> int:
    return min(int(np.ceil(0.1 * x)), 25)


def hyperopt_default_gamma(x: int) -> int:
    return min(int(np.ceil(0.25 * np.sqrt(x))), 25)


def default_weights(x: int) -> np.ndarray:
    if x == 0:
        return np.asarray([])
    elif x < 25:
        return np.ones(x)
    else:
        ramp = np.linspace(1.0 / x, 1.0, num=x - 25)
        flat = np.ones(25)
        return np.concatenate([ramp, flat], axis=0)


[docs]class TPESampler(BaseSampler): """Sampler using TPE (Tree-structured Parzen Estimator) algorithm. This sampler is based on *independent sampling*. See also :class:`~optuna.samplers.BaseSampler` for more details of 'independent sampling'. On each trial, for each parameter, TPE fits one Gaussian Mixture Model (GMM) ``l(x)`` to the set of parameter values associated with the best objective values, and another GMM ``g(x)`` to the remaining parameter values. It chooses the parameter value ``x`` that maximizes the ratio ``l(x)/g(x)``. For further information about TPE algorithm, please refer to the following papers: - `Algorithms for Hyper-Parameter Optimization <https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf>`_ - `Making a Science of Model Search: Hyperparameter Optimization in Hundreds of Dimensions for Vision Architectures <http://proceedings.mlr.press/v28/bergstra13.pdf>`_ - `Multiobjective tree-structured parzen estimator for computationally expensive optimization problems <https://dl.acm.org/doi/10.1145/3377930.3389817>`_ - `Multiobjective Tree-Structured Parzen Estimator <https://doi.org/10.1613/jair.1.13188>`_ Example: .. testcode:: import optuna from optuna.samplers import TPESampler def objective(trial): x = trial.suggest_float("x", -10, 10) return x**2 study = optuna.create_study(sampler=TPESampler()) study.optimize(objective, n_trials=10) Args: consider_prior: Enhance the stability of Parzen estimator by imposing a Gaussian prior when :obj:`True`. The prior is only effective if the sampling distribution is either :class:`~optuna.distributions.FloatDistribution`, or :class:`~optuna.distributions.IntDistribution`. prior_weight: The weight of the prior. This argument is used in :class:`~optuna.distributions.FloatDistribution`, :class:`~optuna.distributions.IntDistribution`, and :class:`~optuna.distributions.CategoricalDistribution`. consider_magic_clip: Enable a heuristic to limit the smallest variances of Gaussians used in the Parzen estimator. consider_endpoints: Take endpoints of domains into account when calculating variances of Gaussians in Parzen estimator. See the original paper for details on the heuristics to calculate the variances. n_startup_trials: The random sampling is used instead of the TPE algorithm until the given number of trials finish in the same study. n_ei_candidates: Number of candidate samples used to calculate the expected improvement. gamma: A function that takes the number of finished trials and returns the number of trials to form a density function for samples with low grains. See the original paper for more details. weights: A function that takes the number of finished trials and returns a weight for them. See `Making a Science of Model Search: Hyperparameter Optimization in Hundreds of Dimensions for Vision Architectures <http://proceedings.mlr.press/v28/bergstra13.pdf>`_ for more details. .. note:: In the multi-objective case, this argument is only used to compute the weights of bad trials, i.e., trials to construct `g(x)` in the `paper <https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf>`_ ). The weights of good trials, i.e., trials to construct `l(x)`, are computed by a rule based on the hypervolume contribution proposed in the `paper of MOTPE <https://dl.acm.org/doi/10.1145/3377930.3389817>`_. seed: Seed for random number generator. multivariate: If this is :obj:`True`, the multivariate TPE is used when suggesting parameters. The multivariate TPE is reported to outperform the independent TPE. See `BOHB: Robust and Efficient Hyperparameter Optimization at Scale <http://proceedings.mlr.press/v80/falkner18a.html>`_ for more details. .. note:: Added in v2.2.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v2.2.0. group: If this and ``multivariate`` are :obj:`True`, the multivariate TPE with the group decomposed search space is used when suggesting parameters. The sampling algorithm decomposes the search space based on past trials and samples from the joint distribution in each decomposed subspace. The decomposed subspaces are a partition of the whole search space. Each subspace is a maximal subset of the whole search space, which satisfies the following: for a trial in completed trials, the intersection of the subspace and the search space of the trial becomes subspace itself or an empty set. Sampling from the joint distribution on the subspace is realized by multivariate TPE. If ``group`` is :obj:`True`, ``multivariate`` must be :obj:`True` as well. .. note:: Added in v2.8.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v2.8.0. Example: .. testcode:: import optuna def objective(trial): x = trial.suggest_categorical("x", ["A", "B"]) if x == "A": return trial.suggest_float("y", -10, 10) else: return trial.suggest_int("z", -10, 10) sampler = optuna.samplers.TPESampler(multivariate=True, group=True) study = optuna.create_study(sampler=sampler) study.optimize(objective, n_trials=10) warn_independent_sampling: If this is :obj:`True` and ``multivariate=True``, a warning message is emitted when the value of a parameter is sampled by using an independent sampler. If ``multivariate=False``, this flag has no effect. constant_liar: If :obj:`True`, penalize running trials to avoid suggesting parameter configurations nearby. .. note:: Abnormally terminated trials often leave behind a record with a state of ``RUNNING`` in the storage. Such "zombie" trial parameters will be avoided by the constant liar algorithm during subsequent sampling. When using an :class:`~optuna.storages.RDBStorage`, it is possible to enable the ``heartbeat_interval`` to change the records for abnormally terminated trials to ``FAIL``. .. note:: It is recommended to set this value to :obj:`True` during distributed optimization to avoid having multiple workers evaluating similar parameter configurations. In particular, if each objective function evaluation is costly and the durations of the running states are significant, and/or the number of workers is high. .. note:: This feature can be used for only single-objective optimization; this argument is ignored for multi-objective optimization. .. note:: Added in v2.8.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v2.8.0. constraints_func: An optional function that computes the objective constraints. It must take a :class:`~optuna.trial.FrozenTrial` and return the constraints. The return value must be a sequence of :obj:`float` s. A value strictly larger than 0 means that a constraints is violated. A value equal to or smaller than 0 is considered feasible. If ``constraints_func`` returns more than one value for a trial, that trial is considered feasible if and only if all values are equal to 0 or smaller. The ``constraints_func`` will be evaluated after each successful trial. The function won't be called when trials fail or they are pruned, but this behavior is subject to change in the future releases. .. note:: Added in v3.0.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v3.0.0. """ def __init__( self, consider_prior: bool = True, prior_weight: float = 1.0, consider_magic_clip: bool = True, consider_endpoints: bool = False, n_startup_trials: int = 10, n_ei_candidates: int = 24, gamma: Callable[[int], int] = default_gamma, weights: Callable[[int], np.ndarray] = default_weights, seed: Optional[int] = None, *, multivariate: bool = False, group: bool = False, warn_independent_sampling: bool = True, constant_liar: bool = False, constraints_func: Optional[Callable[[FrozenTrial], Sequence[float]]] = None, ) -> None: self._parzen_estimator_parameters = _ParzenEstimatorParameters( consider_prior, prior_weight, consider_magic_clip, consider_endpoints, weights, multivariate, ) self._prior_weight = prior_weight self._n_startup_trials = n_startup_trials self._n_ei_candidates = n_ei_candidates self._gamma = gamma self._weights = weights self._warn_independent_sampling = warn_independent_sampling self._rng = np.random.RandomState(seed) self._random_sampler = RandomSampler(seed=seed) self._multivariate = multivariate self._group = group self._group_decomposed_search_space: Optional[_GroupDecomposedSearchSpace] = None self._search_space_group: Optional[_SearchSpaceGroup] = None self._search_space = IntersectionSearchSpace(include_pruned=True) self._constant_liar = constant_liar self._constraints_func = constraints_func if multivariate: warnings.warn( "``multivariate`` option is an experimental feature." " The interface can change in the future.", ExperimentalWarning, ) if group: if not multivariate: raise ValueError( "``group`` option can only be enabled when ``multivariate`` is enabled." ) warnings.warn( "``group`` option is an experimental feature." " The interface can change in the future.", ExperimentalWarning, ) self._group_decomposed_search_space = _GroupDecomposedSearchSpace(True) if constant_liar: warnings.warn( "``constant_liar`` option is an experimental feature." " The interface can change in the future.", ExperimentalWarning, ) if constraints_func is not None: warnings.warn( "The ``constraints_func`` option is an experimental feature." " The interface can change in the future.", ExperimentalWarning, )
[docs] def reseed_rng(self) -> None: self._rng.seed() self._random_sampler.reseed_rng()
[docs] def infer_relative_search_space( self, study: Study, trial: FrozenTrial ) -> Dict[str, BaseDistribution]: if not self._multivariate: return {} search_space: Dict[str, BaseDistribution] = {} if self._group: assert self._group_decomposed_search_space is not None self._search_space_group = self._group_decomposed_search_space.calculate(study) for sub_space in self._search_space_group.search_spaces: # Sort keys because Python's string hashing is nondeterministic. for name, distribution in sorted(sub_space.items()): if distribution.single(): continue search_space[name] = distribution return search_space for name, distribution in self._search_space.calculate(study).items(): if distribution.single(): continue search_space[name] = distribution return search_space
def _log_independent_sampling( self, n_complete_trials: int, trial: FrozenTrial, param_name: str ) -> None: if self._warn_independent_sampling and self._multivariate: # The first trial samples independently. if n_complete_trials >= max(self._n_startup_trials, 1): _logger.warning( f"The parameter '{param_name}' in trial#{trial.number} is sampled " "independently instead of being sampled by multivariate TPE sampler. " "(optimization performance may be degraded). " "You can suppress this warning by setting `warn_independent_sampling` " "to `False` in the constructor of `TPESampler`, " "if this independent sampling is intended behavior." )
[docs] def sample_relative( self, study: Study, trial: FrozenTrial, search_space: Dict[str, BaseDistribution] ) -> Dict[str, Any]: if self._group: assert self._search_space_group is not None params = {} for sub_space in self._search_space_group.search_spaces: search_space = {} # Sort keys because Python's string hashing is nondeterministic. for name, distribution in sorted(sub_space.items()): if not distribution.single(): search_space[name] = distribution params.update(self._sample_relative(study, trial, search_space)) return params else: return self._sample_relative(study, trial, search_space)
def _sample_relative( self, study: Study, trial: FrozenTrial, search_space: Dict[str, BaseDistribution] ) -> Dict[str, Any]: if search_space == {}: return {} param_names = list(search_space.keys()) values, scores, violations = _get_observation_pairs( study, param_names, self._constant_liar, self._constraints_func is not None, ) # If the number of samples is insufficient, we run random trial. n = sum(s < float("inf") for s, v in scores) # Ignore running trials. if n < self._n_startup_trials: return {} # We divide data into below and above. indices_below, indices_above = _split_observation_pairs(scores, self._gamma(n), violations) # `None` items are intentionally converted to `nan` and then filtered out. # For `nan` conversion, the dtype must be float. # `None` items appear when `group=True` or `constant_liar=True`. config_values = {k: np.asarray(v, dtype=float) for k, v in values.items()} param_mask = np.all(~np.isnan(list(config_values.values())), axis=0) param_mask_below, param_mask_above = param_mask[indices_below], param_mask[indices_above] below = {k: v[indices_below[param_mask_below]] for k, v in config_values.items()} above = {k: v[indices_above[param_mask_above]] for k, v in config_values.items()} # We then sample by maximizing log likelihood ratio. if study._is_multi_objective(): weights_below = _calculate_weights_below_for_multi_objective( scores, indices_below, violations )[param_mask_below] mpe_below = _ParzenEstimator( below, search_space, self._parzen_estimator_parameters, weights_below ) else: mpe_below = _ParzenEstimator(below, search_space, self._parzen_estimator_parameters) mpe_above = _ParzenEstimator(above, search_space, self._parzen_estimator_parameters) samples_below = mpe_below.sample(self._rng, self._n_ei_candidates) log_likelihoods_below = mpe_below.log_pdf(samples_below) log_likelihoods_above = mpe_above.log_pdf(samples_below) ret = TPESampler._compare(samples_below, log_likelihoods_below, log_likelihoods_above) for param_name, dist in search_space.items(): ret[param_name] = dist.to_external_repr(ret[param_name]) return ret
[docs] def sample_independent( self, study: Study, trial: FrozenTrial, param_name: str, param_distribution: BaseDistribution, ) -> Any: values, scores, violations = _get_observation_pairs( study, [param_name], self._constant_liar, self._constraints_func is not None, ) n = sum(s < float("inf") for s, v in scores) # Ignore running trials. # Avoid independent warning at the first sampling of `param_name` when `group=True`. if any(param is not None for param in values[param_name]): self._log_independent_sampling(n, trial, param_name) if n < self._n_startup_trials: return self._random_sampler.sample_independent( study, trial, param_name, param_distribution ) indices_below, indices_above = _split_observation_pairs(scores, self._gamma(n), violations) # `None` items are intentionally converted to `nan` and then filtered out. # For `nan` conversion, the dtype must be float. config_value = np.asarray(values[param_name], dtype=float) param_mask = ~np.isnan(config_value) param_mask_below, param_mask_above = param_mask[indices_below], param_mask[indices_above] below = {param_name: config_value[indices_below[param_mask_below]]} above = {param_name: config_value[indices_above[param_mask_above]]} if study._is_multi_objective(): weights_below = _calculate_weights_below_for_multi_objective( scores, indices_below, violations )[param_mask_below] mpe_below = _ParzenEstimator( below, {param_name: param_distribution}, self._parzen_estimator_parameters, weights_below, ) else: mpe_below = _ParzenEstimator( below, {param_name: param_distribution}, self._parzen_estimator_parameters ) mpe_above = _ParzenEstimator( above, {param_name: param_distribution}, self._parzen_estimator_parameters ) samples_below = mpe_below.sample(self._rng, self._n_ei_candidates) log_likelihoods_below = mpe_below.log_pdf(samples_below) log_likelihoods_above = mpe_above.log_pdf(samples_below) ret = TPESampler._compare(samples_below, log_likelihoods_below, log_likelihoods_above) return param_distribution.to_external_repr(ret[param_name])
@classmethod def _compare( cls, samples: Dict[str, np.ndarray], log_l: np.ndarray, log_g: np.ndarray, ) -> Dict[str, Union[float, int]]: sample_size = next(iter(samples.values())).size if sample_size: score = log_l - log_g if sample_size != score.size: raise ValueError( "The size of the 'samples' and that of the 'score' " "should be same. " "But (samples.size, score.size) = ({}, {})".format(sample_size, score.size) ) best = np.argmax(score) return {k: v[best].item() for k, v in samples.items()} else: raise ValueError( "The size of 'samples' should be more than 0." "But samples.size = {}".format(sample_size) )
[docs] @staticmethod def hyperopt_parameters() -> Dict[str, Any]: """Return the the default parameters of hyperopt (v0.1.2). :class:`~optuna.samplers.TPESampler` can be instantiated with the parameters returned by this method. Example: Create a :class:`~optuna.samplers.TPESampler` instance with the default parameters of `hyperopt <https://github.com/hyperopt/hyperopt/tree/0.1.2>`_. .. testcode:: import optuna from optuna.samplers import TPESampler def objective(trial): x = trial.suggest_float("x", -10, 10) return x**2 sampler = TPESampler(**TPESampler.hyperopt_parameters()) study = optuna.create_study(sampler=sampler) study.optimize(objective, n_trials=10) Returns: A dictionary containing the default parameters of hyperopt. """ return { "consider_prior": True, "prior_weight": 1.0, "consider_magic_clip": True, "consider_endpoints": False, "n_startup_trials": 20, "n_ei_candidates": 24, "gamma": hyperopt_default_gamma, "weights": default_weights, }
[docs] def after_trial( self, study: Study, trial: FrozenTrial, state: TrialState, values: Optional[Sequence[float]], ) -> None: assert state in [TrialState.COMPLETE, TrialState.FAIL, TrialState.PRUNED] if self._constraints_func is not None: _process_constraints_after_trial(self._constraints_func, study, trial, state) self._random_sampler.after_trial(study, trial, state, values)
def _calculate_nondomination_rank(loss_vals: np.ndarray) -> np.ndarray: ranks = np.full(len(loss_vals), -1) num_unranked = len(loss_vals) rank = 0 domination_mat = np.all(loss_vals[:, None, :] >= loss_vals[None, :, :], axis=2) & np.any( loss_vals[:, None, :] > loss_vals[None, :, :], axis=2 ) while num_unranked > 0: counts = np.sum((ranks == -1)[None, :] & domination_mat, axis=1) num_unranked -= np.sum((counts == 0) & (ranks == -1)) ranks[(counts == 0) & (ranks == -1)] = rank rank += 1 return ranks def _get_observation_pairs( study: Study, param_names: List[str], constant_liar: bool = False, # TODO(hvy): Remove default value and fix unit tests. constraints_enabled: bool = False, ) -> Tuple[ Dict[str, List[Optional[float]]], List[Tuple[float, List[float]]], Optional[List[float]], ]: """Get observation pairs from the study. This function collects observation pairs from the complete or pruned trials of the study. In addition, if ``constant_liar`` is :obj:`True`, the running trials are considered. The values for trials that don't contain the parameter in the ``param_names`` are skipped. An observation pair fundamentally consists of a parameter value and an objective value. However, due to the pruning mechanism of Optuna, final objective values are not always available. Therefore, this function uses intermediate values in addition to the final ones, and reports the value with its step count as ``(-step, value)``. Consequently, the structure of the observation pair is as follows: ``(param_value, (-step, value))``. The second element of an observation pair is used to rank observations in ``_split_observation_pairs`` method (i.e., observations are sorted lexicographically by ``(-step, value)``). When ``constraints_enabled`` is :obj:`True`, 1-dimensional violation values are returned as the third element (:obj:`None` otherwise). Each value is a float of 0 or greater and a trial is feasible if and only if its violation score is 0. """ signs = [] for d in study.directions: if d == StudyDirection.MINIMIZE: signs.append(1) else: signs.append(-1) states: Container[TrialState] if constant_liar: states = (TrialState.COMPLETE, TrialState.PRUNED, TrialState.RUNNING) else: states = (TrialState.COMPLETE, TrialState.PRUNED) scores = [] values: Dict[str, List[Optional[float]]] = {param_name: [] for param_name in param_names} violations: Optional[List[float]] = [] if constraints_enabled else None for trial in study._get_trials(deepcopy=False, states=states, use_cache=not constant_liar): # We extract score from the trial. if trial.state is TrialState.COMPLETE: if trial.values is None: continue score = (-float("inf"), [sign * v for sign, v in zip(signs, trial.values)]) elif trial.state is TrialState.PRUNED: if study._is_multi_objective(): continue if len(trial.intermediate_values) > 0: step, intermediate_value = max(trial.intermediate_values.items()) if math.isnan(intermediate_value): score = (-step, [float("inf")]) else: score = (-step, [signs[0] * intermediate_value]) else: score = (1, [0.0]) elif trial.state is TrialState.RUNNING: if study._is_multi_objective(): continue assert constant_liar score = (float("inf"), [signs[0] * float("inf")]) else: assert False scores.append(score) # We extract param_value from the trial. for param_name in param_names: param_value: Optional[float] if param_name in trial.params: distribution = trial.distributions[param_name] param_value = distribution.to_internal_repr(trial.params[param_name]) else: param_value = None values[param_name].append(param_value) if constraints_enabled: assert violations is not None if trial.state != TrialState.RUNNING: constraint = trial.system_attrs.get(_CONSTRAINTS_KEY) if constraint is None: warnings.warn( f"Trial {trial.number} does not have constraint values." " It will be treated as a lower priority than other trials." ) violation = float("inf") else: # Violation values of infeasible dimensions are summed up. violation = sum(v for v in constraint if v > 0) violations.append(violation) else: violations.append(float("inf")) return values, scores, violations def _split_observation_pairs( loss_vals: List[Tuple[float, List[float]]], n_below: int, violations: Optional[List[float]], ) -> Tuple[np.ndarray, np.ndarray]: # When constrains is not None, trials are split into below and above # according to the following rules. # 1. Feasible trials are better than infeasible trials. # 2. Infeasible trials are sorted by sum of how much they violate each constraint. # 3. Feasible trials are sorted by loss_vals. if violations is not None: violation_1d = np.array(violations, dtype=float) idx = violation_1d.argsort(kind="stable") if n_below >= len(idx) or violation_1d[idx[n_below]] > 0: # Below is filled by all feasible trials and trials with smaller violation values. indices_below = idx[:n_below] indices_above = idx[n_below:] else: # All trials in below are feasible. # Feasible trials with smaller loss_vals are selected. (feasible_idx,) = (violation_1d == 0).nonzero() (infeasible_idx,) = (violation_1d > 0).nonzero() assert len(feasible_idx) >= n_below feasible_below, feasible_above = _split_observation_pairs( [loss_vals[i] for i in feasible_idx], n_below, None ) indices_below = feasible_idx[feasible_below] indices_above = np.concatenate([feasible_idx[feasible_above], infeasible_idx]) # `np.sort` is used to keep chronological order. return np.sort(indices_below), np.sort(indices_above) n_objectives = 1 if len(loss_vals) > 0: n_objectives = len(loss_vals[0][1]) if n_objectives <= 1: loss_values = np.asarray( [(s, v[0]) for s, v in loss_vals], dtype=[("step", float), ("score", float)] ) index_loss_ascending = np.argsort(loss_values, kind="stable") # `np.sort` is used to keep chronological order. indices_below = np.sort(index_loss_ascending[:n_below]) indices_above = np.sort(index_loss_ascending[n_below:]) else: # Multi-objective TPE does not support pruning, so it ignores the ``step``. lvals = np.asarray([v for _, v in loss_vals]) # Solving HSSP for variables number of times is a waste of time. nondomination_ranks = _calculate_nondomination_rank(lvals) assert 0 <= n_below <= len(lvals) indices = np.array(range(len(lvals))) indices_below = np.empty(n_below, dtype=int) # Nondomination rank-based selection i = 0 last_idx = 0 while last_idx < n_below and last_idx + sum(nondomination_ranks == i) <= n_below: length = indices[nondomination_ranks == i].shape[0] indices_below[last_idx : last_idx + length] = indices[nondomination_ranks == i] last_idx += length i += 1 # Hypervolume subset selection problem (HSSP)-based selection subset_size = n_below - last_idx if subset_size > 0: rank_i_lvals = lvals[nondomination_ranks == i] rank_i_indices = indices[nondomination_ranks == i] worst_point = np.max(rank_i_lvals, axis=0) reference_point = np.maximum(1.1 * worst_point, 0.9 * worst_point) reference_point[reference_point == 0] = EPS selected_indices = _solve_hssp( rank_i_lvals, rank_i_indices, subset_size, reference_point ) indices_below[last_idx:] = selected_indices indices_above = np.setdiff1d(indices, indices_below) return indices_below, indices_above def _calculate_weights_below_for_multi_objective( loss_vals: List[Tuple[float, List[float]]], indices: np.ndarray, violations: Optional[List[float]], ) -> np.ndarray: if violations is None: feasible_mask = np.ones(len(indices), dtype=bool) else: # Hypervolume contributions are calculated only using feasible trials. feasible_mask = np.array(violations, dtype=float)[indices] == 0 # Multi-objective TPE does not support pruning, so it ignores the ``step``. lvals = np.asarray([v for _, v in loss_vals])[indices[feasible_mask]] # Calculate weights based on hypervolume contributions. n_below = len(lvals) weights_below: np.ndarray if n_below == 0: weights_below = np.asarray([]) elif n_below == 1: weights_below = np.asarray([1.0]) else: worst_point = np.max(lvals, axis=0) reference_point = np.maximum(1.1 * worst_point, 0.9 * worst_point) reference_point[reference_point == 0] = EPS hv = WFG().compute(lvals, reference_point) indices_mat = ~np.eye(n_below).astype(bool) contributions = np.asarray( [hv - WFG().compute(lvals[indices_mat[i]], reference_point) for i in range(n_below)] ) contributions += EPS weights_below = np.clip(contributions / np.max(contributions), 0, 1) # For now, EPS weight is assigned to infeasible trials. weights_below_all = np.full(len(indices), EPS) weights_below_all[feasible_mask] = weights_below return weights_below_all