Source code for optuna.samplers._tpe.sampler

from __future__ import annotations

import math
from typing import Any
from typing import Callable
from typing import cast
from typing import Dict
from typing import Optional
from typing import Sequence
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.distributions import CategoricalChoiceType
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._lazy_random_state import LazyRandomState
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>`_ - `Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance <https://arxiv.org/abs/2304.11127>`_ For multi-objective TPE (MOTPE), please refer to the following papers: - `Multiobjective Tree-Structured Parzen Estimator for Computationally Expensive Optimization Problems <https://doi.org/10.1145/3377930.3389817>`_ - `Multiobjective Tree-Structured Parzen Estimator <https://doi.org/10.1613/jair.1.13188>`_ Example: An example of a single-objective optimization is as follows: .. 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) .. note:: :class:`~optuna.samplers.TPESampler` can handle a multi-objective task as well and the following shows an example: .. testcode:: import optuna def objective(trial): x = trial.suggest_float("x", -100, 100) y = trial.suggest_categorical("y", [-1, 0, 1]) f1 = x**2 + y f2 = -((x - 2) ** 2 + y) return f1, f2 # We minimize the first objective and maximize the second objective. sampler = optuna.samplers.TPESampler() study = optuna.create_study(directions=["minimize", "maximize"], sampler=sampler) study.optimize(objective, n_trials=100) 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://doi.org/10.1613/jair.1.13188>`_. 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:: 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. categorical_distance_func: A dictionary of distance functions for categorical parameters. The key is the name of the categorical parameter and the value is a distance function that takes two :class:`~optuna.distributions.CategoricalChoiceType` s and returns a :obj:`float` value. The distance function must return a non-negative value. While categorical choices are handled equally by default, this option allows users to specify prior knowledge on the structure of categorical parameters. When specified, categorical choices closer to current best choices are more likely to be sampled. .. note:: Added in v3.4.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v3.4.0. """ 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, categorical_distance_func: Optional[ dict[str, Callable[[CategoricalChoiceType, CategoricalChoiceType], float]] ] = None, ) -> None: self._parzen_estimator_parameters = _ParzenEstimatorParameters( consider_prior, prior_weight, consider_magic_clip, consider_endpoints, weights, multivariate, categorical_distance_func or {}, ) self._n_startup_trials = n_startup_trials self._n_ei_candidates = n_ei_candidates self._gamma = gamma self._warn_independent_sampling = warn_independent_sampling self._rng = LazyRandomState(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, ) if categorical_distance_func is not None: warnings.warn( "The ``categorical_distance_func`` option is an experimental feature." " The interface can change in the future.", ExperimentalWarning, )
[docs] def reseed_rng(self) -> None: self._rng.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
[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 {} states = (TrialState.COMPLETE, TrialState.PRUNED) trials = study._get_trials(deepcopy=False, states=states, use_cache=True) # If the number of samples is insufficient, we run random trial. if len(trials) < self._n_startup_trials: return {} return self._sample(study, trial, search_space)
[docs] def sample_independent( self, study: Study, trial: FrozenTrial, param_name: str, param_distribution: BaseDistribution, ) -> Any: states = (TrialState.COMPLETE, TrialState.PRUNED) trials = study._get_trials(deepcopy=False, states=states, use_cache=True) # If the number of samples is insufficient, we run random trial. if len(trials) < self._n_startup_trials: return self._random_sampler.sample_independent( study, trial, param_name, param_distribution ) if self._warn_independent_sampling and self._multivariate: # Avoid independent warning at the first sampling of `param_name`. if any(param_name in trial.params for trial in trials): _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." ) return self._sample(study, trial, {param_name: param_distribution})[param_name]
def _get_internal_repr( self, trials: list[FrozenTrial], search_space: dict[str, BaseDistribution] ) -> dict[str, np.ndarray]: values: dict[str, list[float]] = {param_name: [] for param_name in search_space} for trial in trials: if all((param_name in trial.params) for param_name in search_space): for param_name in search_space: param = trial.params[param_name] distribution = trial.distributions[param_name] values[param_name].append(distribution.to_internal_repr(param)) return {k: np.asarray(v) for k, v in values.items()} def _sample( self, study: Study, trial: FrozenTrial, search_space: Dict[str, BaseDistribution] ) -> Dict[str, Any]: if self._constant_liar: states = [TrialState.COMPLETE, TrialState.PRUNED, TrialState.RUNNING] else: states = [TrialState.COMPLETE, TrialState.PRUNED] use_cache = not self._constant_liar trials = study._get_trials(deepcopy=False, states=states, use_cache=use_cache) # We divide data into below and above. n = sum(trial.state != TrialState.RUNNING for trial in trials) # Ignore running trials. below_trials, above_trials = _split_trials( study, trials, self._gamma(n), self._constraints_func is not None, ) mpe_below = self._build_parzen_estimator( study, search_space, below_trials, handle_below=True ) mpe_above = self._build_parzen_estimator( study, search_space, above_trials, handle_below=False ) samples_below = mpe_below.sample(self._rng.rng, self._n_ei_candidates) acq_func_vals = self._compute_acquisition_func(samples_below, mpe_below, mpe_above) ret = TPESampler._compare(samples_below, acq_func_vals) for param_name, dist in search_space.items(): ret[param_name] = dist.to_external_repr(ret[param_name]) return ret def _build_parzen_estimator( self, study: Study, search_space: dict[str, BaseDistribution], trials: list[FrozenTrial], handle_below: bool, ) -> _ParzenEstimator: observations = self._get_internal_repr(trials, search_space) if handle_below and study._is_multi_objective(): param_mask_below = [] for trial in trials: param_mask_below.append( all((param_name in trial.params) for param_name in search_space) ) weights_below = _calculate_weights_below_for_multi_objective( study, trials, self._constraints_func )[param_mask_below] mpe = _ParzenEstimator( observations, search_space, self._parzen_estimator_parameters, weights_below ) else: mpe = _ParzenEstimator(observations, search_space, self._parzen_estimator_parameters) return mpe def _compute_acquisition_func( self, samples: dict[str, np.ndarray], mpe_below: _ParzenEstimator, mpe_above: _ParzenEstimator, ) -> np.ndarray: log_likelihoods_below = mpe_below.log_pdf(samples) log_likelihoods_above = mpe_above.log_pdf(samples) acq_func_vals = log_likelihoods_below - log_likelihoods_above return acq_func_vals @classmethod def _compare( cls, samples: Dict[str, np.ndarray], acquisition_func_vals: np.ndarray, ) -> dict[str, int | float]: sample_size = next(iter(samples.values())).size if sample_size == 0: raise ValueError(f"The size of `samples` must be positive, but got {sample_size}.") if sample_size != acquisition_func_vals.size: raise ValueError( "The sizes of `samples` and `acquisition_func_vals` must be same, but got " "(samples.size, acquisition_func_vals.size) = " f"({sample_size}, {acquisition_func_vals.size})." ) best_idx = np.argmax(acquisition_func_vals) return {k: v[best_idx].item() for k, v in samples.items()}
[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 before_trial(self, study: Study, trial: FrozenTrial) -> None: self._random_sampler.before_trial(study, trial)
[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, n_below: int) -> np.ndarray: ranks = np.full(len(loss_vals), -1) num_ranked = 0 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_ranked < n_below: counts = np.sum((ranks == -1)[None, :] & domination_mat, axis=1) num_ranked += np.sum((counts == 0) & (ranks == -1)) ranks[(counts == 0) & (ranks == -1)] = rank rank += 1 return ranks def _split_trials( study: Study, trials: list[FrozenTrial], n_below: int, constraints_enabled: bool, ) -> tuple[list[FrozenTrial], list[FrozenTrial]]: complete_trials = [] pruned_trials = [] running_trials = [] infeasible_trials = [] for trial in trials: if constraints_enabled and _get_infeasible_trial_score(trial) > 0: infeasible_trials.append(trial) elif trial.state == TrialState.COMPLETE: complete_trials.append(trial) elif trial.state == TrialState.PRUNED: pruned_trials.append(trial) elif trial.state == TrialState.RUNNING: running_trials.append(trial) else: assert False # We divide data into below and above. below_complete, above_complete = _split_complete_trials(complete_trials, study, n_below) # This ensures `n_below` is non-negative to prevent unexpected trial splits. n_below = max(0, n_below - len(below_complete)) below_pruned, above_pruned = _split_pruned_trials(pruned_trials, study, n_below) # This ensures `n_below` is non-negative to prevent unexpected trial splits. n_below = max(0, n_below - len(below_pruned)) below_infeasible, above_infeasible = _split_infeasible_trials(infeasible_trials, n_below) below_trials = below_complete + below_pruned + below_infeasible above_trials = above_complete + above_pruned + above_infeasible + running_trials below_trials.sort(key=lambda trial: trial.number) above_trials.sort(key=lambda trial: trial.number) return below_trials, above_trials def _split_complete_trials( trials: Sequence[FrozenTrial], study: Study, n_below: int ) -> tuple[list[FrozenTrial], list[FrozenTrial]]: n_below = min(n_below, len(trials)) if len(study.directions) <= 1: return _split_complete_trials_single_objective(trials, study, n_below) else: return _split_complete_trials_multi_objective(trials, study, n_below) def _split_complete_trials_single_objective( trials: Sequence[FrozenTrial], study: Study, n_below: int, ) -> tuple[list[FrozenTrial], list[FrozenTrial]]: if study.direction == StudyDirection.MINIMIZE: sorted_trials = sorted(trials, key=lambda trial: cast(float, trial.value)) else: sorted_trials = sorted(trials, key=lambda trial: cast(float, trial.value), reverse=True) return sorted_trials[:n_below], sorted_trials[n_below:] def _split_complete_trials_multi_objective( trials: Sequence[FrozenTrial], study: Study, n_below: int, ) -> tuple[list[FrozenTrial], list[FrozenTrial]]: if n_below == 0: # The type of trials must be `list`, but not `Sequence`. return [], list(trials) lvals = np.asarray([trial.values for trial in trials]) for i, direction in enumerate(study.directions): if direction == StudyDirection.MAXIMIZE: lvals[:, i] *= -1 # Solving HSSP for variables number of times is a waste of time. nondomination_ranks = _calculate_nondomination_rank(lvals, n_below) 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 below_trials = [] above_trials = [] for index in range(len(trials)): if index in indices_below: below_trials.append(trials[index]) else: above_trials.append(trials[index]) return below_trials, above_trials def _get_pruned_trial_score(trial: FrozenTrial, study: Study) -> tuple[float, float]: if len(trial.intermediate_values) > 0: step, intermediate_value = max(trial.intermediate_values.items()) if math.isnan(intermediate_value): return -step, float("inf") elif study.direction == StudyDirection.MINIMIZE: return -step, intermediate_value else: return -step, -intermediate_value else: return 1, 0.0 def _split_pruned_trials( trials: Sequence[FrozenTrial], study: Study, n_below: int, ) -> tuple[list[FrozenTrial], list[FrozenTrial]]: n_below = min(n_below, len(trials)) sorted_trials = sorted(trials, key=lambda trial: _get_pruned_trial_score(trial, study)) return sorted_trials[:n_below], sorted_trials[n_below:] def _get_infeasible_trial_score(trial: FrozenTrial) -> float: 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." ) return float("inf") else: # Violation values of infeasible dimensions are summed up. return sum(v for v in constraint if v > 0) def _split_infeasible_trials( trials: Sequence[FrozenTrial], n_below: int ) -> tuple[list[FrozenTrial], list[FrozenTrial]]: n_below = min(n_below, len(trials)) sorted_trials = sorted(trials, key=_get_infeasible_trial_score) return sorted_trials[:n_below], sorted_trials[n_below:] def _calculate_weights_below_for_multi_objective( study: Study, below_trials: list[FrozenTrial], constraints_func: Callable[[FrozenTrial], Sequence[float]] | None, ) -> np.ndarray: loss_vals = [] feasible_mask = np.ones(len(below_trials), dtype=bool) for i, trial in enumerate(below_trials): # Hypervolume contributions are calculated only using feasible trials. if constraints_func is not None: if any(constraint > 0 for constraint in constraints_func(trial)): feasible_mask[i] = False continue values = [] for value, direction in zip(trial.values, study.directions): if direction == StudyDirection.MINIMIZE: values.append(value) else: values.append(-value) loss_vals.append(values) lvals = np.asarray(loss_vals, dtype=float) # 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(below_trials), EPS) weights_below_all[feasible_mask] = weights_below return weights_below_all