import math
import numpy as np
import scipy.special
from scipy.stats import truncnorm
from optuna import distributions
from optuna.samplers._tpe.parzen_estimator import _ParzenEstimator
from optuna.samplers._tpe.parzen_estimator import _ParzenEstimatorParameters
from optuna.samplers import BaseSampler
from optuna.samplers import RandomSampler
from optuna.study import StudyDirection
from optuna.trial import TrialState
from optuna import type_checking
if type_checking.TYPE_CHECKING:
from typing import Any # NOQA
from typing import Callable # NOQA
from typing import Dict # NOQA
from typing import List # NOQA
from typing import Optional # NOQA
from typing import Tuple # NOQA
from optuna.distributions import BaseDistribution # NOQA
from optuna.study import Study # NOQA
from optuna.trial import FrozenTrial # NOQA
EPS = 1e-12
def default_gamma(x):
# type: (int) -> int
return min(int(np.ceil(0.1 * x)), 25)
def hyperopt_default_gamma(x):
# type: (int) -> int
return min(int(np.ceil(0.25 * np.sqrt(x))), 25)
def default_weights(x):
# type: (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>`_
Example:
.. testcode::
import optuna
from optuna.samplers import TPESampler
def objective(trial):
x = trial.suggest_uniform('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.UniformDistribution`,
:class:`~optuna.distributions.DiscreteUniformDistribution`,
:class:`~optuna.distributions.LogUniformDistribution`,
:class:`~optuna.distributions.IntUniformDistribution`,
or :class:`~optuna.distributions.IntLogUniformDistribution`.
prior_weight:
The weight of the prior. This argument is used in
:class:`~optuna.distributions.UniformDistribution`,
:class:`~optuna.distributions.DiscreteUniformDistribution`,
:class:`~optuna.distributions.LogUniformDistribution`,
:class:`~optuna.distributions.IntUniformDistribution`,
:class:`~optuna.distributions.IntLogUniformDistribution`, 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.
seed:
Seed for random number generator.
"""
[docs] def __init__(
self,
consider_prior=True, # type: bool
prior_weight=1.0, # type: float
consider_magic_clip=True, # type: bool
consider_endpoints=False, # type: bool
n_startup_trials=10, # type: int
n_ei_candidates=24, # type: int
gamma=default_gamma, # type: Callable[[int], int]
weights=default_weights, # type: Callable[[int], np.ndarray]
seed=None, # type: Optional[int]
):
# type: (...) -> None
self._parzen_estimator_parameters = _ParzenEstimatorParameters(
consider_prior, prior_weight, consider_magic_clip, consider_endpoints, weights
)
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._rng = np.random.RandomState(seed)
self._random_sampler = RandomSampler(seed=seed)
[docs] def reseed_rng(self) -> None:
self._rng = np.random.RandomState()
self._random_sampler.reseed_rng()
[docs] def infer_relative_search_space(self, study, trial):
# type: (Study, FrozenTrial) -> Dict[str, BaseDistribution]
return {}
[docs] def sample_relative(self, study, trial, search_space):
# type: (Study, FrozenTrial, Dict[str, BaseDistribution]) -> Dict[str, Any]
return {}
[docs] def sample_independent(self, study, trial, param_name, param_distribution):
# type: (Study, FrozenTrial, str, BaseDistribution) -> Any
values, scores = _get_observation_pairs(study, param_name, trial)
n = len(values)
if n < self._n_startup_trials:
return self._random_sampler.sample_independent(
study, trial, param_name, param_distribution
)
below_param_values, above_param_values = self._split_observation_pairs(values, scores)
if isinstance(param_distribution, distributions.UniformDistribution):
return self._sample_uniform(param_distribution, below_param_values, above_param_values)
elif isinstance(param_distribution, distributions.LogUniformDistribution):
return self._sample_loguniform(
param_distribution, below_param_values, above_param_values
)
elif isinstance(param_distribution, distributions.DiscreteUniformDistribution):
return self._sample_discrete_uniform(
param_distribution, below_param_values, above_param_values
)
elif isinstance(param_distribution, distributions.IntUniformDistribution):
return self._sample_int(param_distribution, below_param_values, above_param_values)
elif isinstance(param_distribution, distributions.IntLogUniformDistribution):
return self._sample_int_loguniform(
param_distribution, below_param_values, above_param_values
)
elif isinstance(param_distribution, distributions.CategoricalDistribution):
index = self._sample_categorical_index(
param_distribution, below_param_values, above_param_values
)
return param_distribution.choices[index]
else:
distribution_list = [
distributions.UniformDistribution.__name__,
distributions.LogUniformDistribution.__name__,
distributions.DiscreteUniformDistribution.__name__,
distributions.IntUniformDistribution.__name__,
distributions.IntLogUniformDistribution.__name__,
distributions.CategoricalDistribution.__name__,
]
raise NotImplementedError(
"The distribution {} is not implemented. "
"The parameter distribution should be one of the {}".format(
param_distribution, distribution_list
)
)
def _split_observation_pairs(
self,
config_vals, # type: List[Optional[float]]
loss_vals, # type: List[Tuple[float, float]]
):
# type: (...) -> Tuple[np.ndarray, np.ndarray]
config_vals = np.asarray(config_vals)
loss_vals = np.asarray(loss_vals, dtype=[("step", float), ("score", float)])
n_below = self._gamma(len(config_vals))
loss_ascending = np.argsort(loss_vals)
below = config_vals[np.sort(loss_ascending[:n_below])]
below = np.asarray([v for v in below if v is not None], dtype=float)
above = config_vals[np.sort(loss_ascending[n_below:])]
above = np.asarray([v for v in above if v is not None], dtype=float)
return below, above
def _sample_uniform(self, distribution, below, above):
# type: (distributions.UniformDistribution, np.ndarray, np.ndarray) -> float
low = distribution.low
high = distribution.high
return self._sample_numerical(low, high, below, above)
def _sample_loguniform(self, distribution, below, above):
# type: (distributions.LogUniformDistribution, np.ndarray, np.ndarray) -> float
low = distribution.low
high = distribution.high
return self._sample_numerical(low, high, below, above, is_log=True)
def _sample_discrete_uniform(self, distribution, below, above):
# type:(distributions.DiscreteUniformDistribution, np.ndarray, np.ndarray) -> float
q = distribution.q
r = distribution.high - distribution.low
# [low, high] is shifted to [0, r] to align sampled values at regular intervals.
low = 0 - 0.5 * q
high = r + 0.5 * q
# Shift below and above to [0, r]
above -= distribution.low
below -= distribution.low
best_sample = self._sample_numerical(low, high, below, above, q=q) + distribution.low
return min(max(best_sample, distribution.low), distribution.high)
def _sample_int(self, distribution, below, above):
# type: (distributions.IntUniformDistribution, np.ndarray, np.ndarray) -> int
d = distributions.DiscreteUniformDistribution(
low=distribution.low, high=distribution.high, q=distribution.step
)
return int(self._sample_discrete_uniform(d, below, above))
def _sample_int_loguniform(self, distribution, below, above):
# type: (distributions.IntLogUniformDistribution, np.ndarray, np.ndarray) -> int
low = distribution.low - 0.5
high = distribution.high + 0.5
sample = self._sample_numerical(low, high, below, above, is_log=True)
best_sample = np.round(sample)
return int(min(max(best_sample, distribution.low), distribution.high))
def _sample_numerical(
self,
low, # type: float
high, # type: float
below, # type: np.ndarray
above, # type: np.ndarray
q=None, # type: Optional[float]
is_log=False, # type: bool
):
# type: (...) -> float
if is_log:
low = np.log(low)
high = np.log(high)
below = np.log(below)
above = np.log(above)
size = (self._n_ei_candidates,)
parzen_estimator_below = _ParzenEstimator(
mus=below, low=low, high=high, parameters=self._parzen_estimator_parameters
)
samples_below = self._sample_from_gmm(
parzen_estimator=parzen_estimator_below, low=low, high=high, q=q, size=size,
)
log_likelihoods_below = self._gmm_log_pdf(
samples=samples_below,
parzen_estimator=parzen_estimator_below,
low=low,
high=high,
q=q,
)
parzen_estimator_above = _ParzenEstimator(
mus=above, low=low, high=high, parameters=self._parzen_estimator_parameters
)
log_likelihoods_above = self._gmm_log_pdf(
samples=samples_below,
parzen_estimator=parzen_estimator_above,
low=low,
high=high,
q=q,
)
ret = float(
TPESampler._compare(
samples=samples_below, log_l=log_likelihoods_below, log_g=log_likelihoods_above
)[0]
)
return math.exp(ret) if is_log else ret
def _sample_categorical_index(self, distribution, below, above):
# type: (distributions.CategoricalDistribution, np.ndarray, np.ndarray) -> int
choices = distribution.choices
below = list(map(int, below))
above = list(map(int, above))
upper = len(choices)
size = (self._n_ei_candidates,)
weights_below = self._weights(len(below))
counts_below = np.bincount(below, minlength=upper, weights=weights_below)
weighted_below = counts_below + self._prior_weight
weighted_below /= weighted_below.sum()
samples_below = self._sample_from_categorical_dist(weighted_below, size)
log_likelihoods_below = TPESampler._categorical_log_pdf(samples_below, weighted_below)
weights_above = self._weights(len(above))
counts_above = np.bincount(above, minlength=upper, weights=weights_above)
weighted_above = counts_above + self._prior_weight
weighted_above /= weighted_above.sum()
log_likelihoods_above = TPESampler._categorical_log_pdf(samples_below, weighted_above)
return int(
TPESampler._compare(
samples=samples_below, log_l=log_likelihoods_below, log_g=log_likelihoods_above
)[0]
)
def _sample_from_gmm(
self,
parzen_estimator, # type: _ParzenEstimator
low, # type: float
high, # type: float
q=None, # type: Optional[float]
size=(), # type: Tuple
):
# type: (...) -> np.ndarray
weights = parzen_estimator.weights
mus = parzen_estimator.mus
sigmas = parzen_estimator.sigmas
weights, mus, sigmas = map(np.asarray, (weights, mus, sigmas))
if low >= high:
raise ValueError(
"The 'low' should be lower than the 'high'. "
"But (low, high) = ({}, {}).".format(low, high)
)
active = np.argmax(self._rng.multinomial(1, weights, size=size), axis=-1)
trunc_low = (low - mus[active]) / sigmas[active]
trunc_high = (high - mus[active]) / sigmas[active]
while True:
samples = truncnorm.rvs(
trunc_low,
trunc_high,
size=size,
loc=mus[active],
scale=sigmas[active],
random_state=self._rng,
)
if (samples < high).all():
break
if q is None:
return samples
else:
return np.round(samples / q) * q
def _gmm_log_pdf(
self,
samples, # type: np.ndarray
parzen_estimator, # type: _ParzenEstimator
low, # type: float
high, # type: float
q=None, # type: Optional[float]
):
# type: (...) -> np.ndarray
weights = parzen_estimator.weights
mus = parzen_estimator.mus
sigmas = parzen_estimator.sigmas
samples, weights, mus, sigmas = map(np.asarray, (samples, weights, mus, sigmas))
if samples.size == 0:
return np.asarray([], dtype=float)
if weights.ndim != 1:
raise ValueError(
"The 'weights' should be 2-dimension. "
"But weights.shape = {}".format(weights.shape)
)
if mus.ndim != 1:
raise ValueError(
"The 'mus' should be 2-dimension. But mus.shape = {}".format(mus.shape)
)
if sigmas.ndim != 1:
raise ValueError(
"The 'sigmas' should be 2-dimension. But sigmas.shape = {}".format(sigmas.shape)
)
p_accept = np.sum(
weights
* (
TPESampler._normal_cdf(high, mus, sigmas)
- TPESampler._normal_cdf(low, mus, sigmas)
)
)
if q is None:
distance = samples[..., None] - mus
mahalanobis = (distance / np.maximum(sigmas, EPS)) ** 2
Z = np.sqrt(2 * np.pi) * sigmas
coefficient = weights / Z / p_accept
return TPESampler._logsum_rows(-0.5 * mahalanobis + np.log(coefficient))
else:
cdf_func = TPESampler._normal_cdf
upper_bound = np.minimum(samples + q / 2.0, high)
lower_bound = np.maximum(samples - q / 2.0, low)
probabilities = np.sum(
weights[..., None]
* (
cdf_func(upper_bound[None], mus[..., None], sigmas[..., None])
- cdf_func(lower_bound[None], mus[..., None], sigmas[..., None])
),
axis=0,
)
return np.log(probabilities + EPS) - np.log(p_accept + EPS)
def _sample_from_categorical_dist(self, probabilities, size):
# type: (np.ndarray, Tuple[int]) -> np.ndarray
if probabilities.size == 1 and isinstance(probabilities[0], np.ndarray):
probabilities = probabilities[0]
probabilities = np.asarray(probabilities)
if size == (0,):
return np.asarray([], dtype=float)
assert len(size)
assert probabilities.ndim == 1
n_draws = int(np.prod(size))
sample = self._rng.multinomial(n=1, pvals=probabilities, size=int(n_draws))
assert sample.shape == size + (probabilities.size,)
return_val = np.dot(sample, np.arange(probabilities.size))
return_val.shape = size
return return_val
@classmethod
def _categorical_log_pdf(
cls,
sample, # type: np.ndarray
p, # type: np.ndarray
):
# type: (...) -> np.ndarray
if sample.size:
return np.log(np.asarray(p)[sample])
else:
return np.asarray([])
@classmethod
def _compare(cls, samples, log_l, log_g):
# type: (np.ndarray, np.ndarray, np.ndarray) -> np.ndarray
samples, log_l, log_g = map(np.asarray, (samples, log_l, log_g))
if samples.size:
score = log_l - log_g
if samples.size != score.size:
raise ValueError(
"The size of the 'samples' and that of the 'score' "
"should be same. "
"But (samples.size, score.size) = ({}, {})".format(samples.size, score.size)
)
best = np.argmax(score)
return np.asarray([samples[best]] * samples.size)
else:
return np.asarray([])
@classmethod
def _logsum_rows(cls, x):
# type: (np.ndarray) -> np.ndarray
x = np.asarray(x)
m = x.max(axis=1)
return np.log(np.exp(x - m[:, None]).sum(axis=1)) + m
@classmethod
def _normal_cdf(cls, x, mu, sigma):
# type: (float, np.ndarray, np.ndarray) -> np.ndarray
mu, sigma = map(np.asarray, (mu, sigma))
denominator = x - mu
numerator = np.maximum(np.sqrt(2) * sigma, EPS)
z = denominator / numerator
return 0.5 * (1 + scipy.special.erf(z))
@classmethod
def _log_normal_cdf(cls, x, mu, sigma):
# type: (float, np.ndarray, np.ndarray) -> np.ndarray
mu, sigma = map(np.asarray, (mu, sigma))
if x < 0:
raise ValueError("Negative argument is given to _lognormal_cdf. x: {}".format(x))
denominator = np.log(np.maximum(x, EPS)) - mu
numerator = np.maximum(np.sqrt(2) * sigma, EPS)
z = denominator / numerator
return 0.5 + 0.5 * scipy.special.erf(z)
[docs] @staticmethod
def hyperopt_parameters():
# type: () -> 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_uniform('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,
}
def _get_observation_pairs(study, param_name, trial):
# type: (Study, str, FrozenTrial) -> Tuple[List[Optional[float]], List[Tuple[float, float]]]
"""Get observation pairs from the study.
This function collects observation pairs from the complete or pruned trials of the study.
The values for trials that don't contain the parameter named ``param_name`` are set to None.
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)``).
"""
sign = 1
if study.direction == StudyDirection.MAXIMIZE:
sign = -1
values = []
scores = []
for trial in study._storage.get_all_trials(study._study_id, deepcopy=False):
if trial.state is TrialState.COMPLETE and trial.value is not None:
score = (-float("inf"), sign * trial.value)
elif trial.state is TrialState.PRUNED:
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, sign * intermediate_value)
else:
score = (float("inf"), 0.0)
else:
continue
param_value = None # type: Optional[float]
if param_name in trial.params:
distribution = trial.distributions[param_name]
param_value = distribution.to_internal_repr(trial.params[param_name])
values.append(param_value)
scores.append(score)
return values, scores