optuna.samplers.CmaEsSampler

class optuna.samplers.CmaEsSampler(x0=None, sigma0=None, n_startup_trials=1, independent_sampler=None, warn_independent_sampling=True, seed=None, *, consider_pruned_trials=False, restart_strategy=None, popsize=None, inc_popsize=-1, use_separable_cma=False, with_margin=False, lr_adapt=False, source_trials=None)

A sampler using cmaes as the backend.

Example

Optimize a simple quadratic function by using CmaEsSampler.

$ pip install cmaes

import optuna


def objective(trial):
    x = trial.suggest_float("x", -1, 1)
    y = trial.suggest_int("y", -1, 1)
    return x**2 + y


sampler = optuna.samplers.CmaEsSampler()
study = optuna.create_study(sampler=sampler)
study.optimize(objective, n_trials=20)

Please note that this sampler does not support CategoricalDistribution. However, FloatDistribution with step, (suggest_float()) and IntDistribution (suggest_int()) are supported.

If your search space contains categorical parameters, I recommend you to use TPESampler instead. Furthermore, there is room for performance improvements in parallel optimization settings. This sampler cannot use some trials for updating the parameters of multivariate normal distribution.

For further information about CMA-ES algorithm, please refer to the following papers:

• N. Hansen, The CMA Evolution Strategy: A Tutorial. arXiv:1604.00772, 2016.

• A. Auger and N. Hansen. A restart CMA evolution strategy with increasing population size. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), pages 1769–1776. IEEE Press, 2005.

• N. Hansen. Benchmarking a BI-Population CMA-ES on the BBOB-2009 Function Testbed. GECCO Workshop, 2009.

• Raymond Ros, Nikolaus Hansen. A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity. 10th International Conference on Parallel Problem Solving From Nature, Sep 2008, Dortmund, Germany. inria-00287367.

• Masahiro Nomura, Shuhei Watanabe, Youhei Akimoto, Yoshihiko Ozaki, Masaki Onishi. Warm Starting CMA-ES for Hyperparameter Optimization, AAAI. 2021.

• R. Hamano, S. Saito, M. Nomura, S. Shirakawa. CMA-ES with Margin: Lower-Bounding Marginal Probability for Mixed-Integer Black-Box Optimization, GECCO. 2022.

• M. Nomura, Y. Akimoto, I. Ono. CMA-ES with Learning Rate Adaptation: Can CMA-ES with Default Population Size Solve Multimodal and Noisy Problems?, GECCO. 2023.

See also

You can also use optuna_integration.PyCmaSampler which is a sampler using cma library as the backend.

Parameters:

• x0 (dict[str, Any] | None) – A dictionary of an initial parameter values for CMA-ES. By default, the mean of low and high for each distribution is used. Note that x0 is sampled uniformly within the search space domain for each restart if you specify restart_strategy argument.

• sigma0 (float | None) – Initial standard deviation of CMA-ES. By default, sigma0 is set to min_range / 6, where min_range denotes the minimum range of the distributions in the search space.

• seed (int | None) – A random seed for CMA-ES.

• n_startup_trials (int) – The independent sampling is used instead of the CMA-ES algorithm until the given number of trials finish in the same study.

• independent_sampler (BaseSampler | None) –

  A BaseSampler instance that is used for independent sampling. The parameters not contained in the relative search space are sampled by this sampler. The search space for CmaEsSampler is determined by intersection_search_space().

  If None is specified, RandomSampler is used as the default.

  See also

  optuna.samplers module provides built-in independent samplers such as RandomSampler and TPESampler.

• warn_independent_sampling (bool) –

  If this is True, a warning message is emitted when the value of a parameter is sampled by using an independent sampler.

  Note that the parameters of the first trial in a study are always sampled via an independent sampler, so no warning messages are emitted in this case.

• restart_strategy (str | None) –

  Strategy for restarting CMA-ES optimization when converges to a local minimum. If None is given, CMA-ES will not restart (default). If ‘ipop’ is given, CMA-ES will restart with increasing population size. if ‘bipop’ is given, CMA-ES will restart with the population size increased or decreased. Please see also inc_popsize parameter.

  Warning

  Deprecated in v4.4.0. restart_strategy argument will be removed in the future. The removal of this feature is currently scheduled for v6.0.0, but this schedule is subject to change. From v4.4.0 onward, restart_strategy automatically falls back to None, and restart_strategy will be supported in OptunaHub. See https://github.com/optuna/optuna/releases/tag/v4.4.0.

• popsize (int | None) – A population size of CMA-ES.

• inc_popsize (int) –

  Multiplier for increasing population size before each restart. This argument will be used when restart_strategy = 'ipop' or restart_strategy = 'bipop' is specified.

  Warning

  Deprecated in v4.4.0. inc_popsize argument will be removed in the future. The removal of this feature is currently scheduled for v6.0.0, but this schedule is subject to change. From v4.4.0 onward, inc_popsize is no longer utilized within Optuna, and inc_popsize will be supported in OptunaHub. See https://github.com/optuna/optuna/releases/tag/v4.4.0.

• consider_pruned_trials (bool) –

  If this is True, the PRUNED trials are considered for sampling.

  Note

  Added in v2.0.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v2.0.0.

  Note

  It is suggested to set this flag False when the MedianPruner is used. On the other hand, it is suggested to set this flag True when the HyperbandPruner is used. Please see the benchmark result for the details.

• use_separable_cma (bool) –

  If this is True, the covariance matrix is constrained to be diagonal. Due to reduce the model complexity, the learning rate for the covariance matrix is increased. Consequently, this algorithm outperforms CMA-ES on separable functions.

  Note

  Added in v2.6.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v2.6.0.

• with_margin (bool) –

  If this is True, CMA-ES with margin is used. This algorithm prevents samples in each discrete distribution (FloatDistribution with step and IntDistribution) from being fixed to a single point. Currently, this option cannot be used with use_separable_cma=True.

  Note

  Added in v3.1.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v3.1.0.

• lr_adapt (bool) –

  If this is True, CMA-ES with learning rate adaptation is used. This algorithm focuses on working well on multimodal and/or noisy problems with default settings. Currently, this option cannot be used with use_separable_cma=True or with_margin=True.

  Note

  Added in v3.3.0 or later, as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v3.3.0.

• source_trials (list[FrozenTrial] | None) –

  This option is for Warm Starting CMA-ES, a method to transfer prior knowledge on similar HPO tasks through the initialization of CMA-ES. This method estimates a promising distribution from source_trials and generates the parameter of multivariate gaussian distribution. Please note that it is prohibited to use x0, sigma0, or use_separable_cma argument together.

  Note

  Added in v2.6.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v2.6.0.

Methods

after_trial(study, trial, state, values)	Trial post-processing.
before_trial(study, trial)	Trial pre-processing.
infer_relative_search_space(study, trial)	Infer the search space that will be used by relative sampling in the target trial.
reseed_rng()	Reseed sampler's random number generator.
sample_independent(study, trial, param_name, ...)	Sample a parameter for a given distribution.
sample_relative(study, trial, search_space)	Sample parameters in a given search space.

after_trial(study, trial, state, values)

Trial post-processing.

This method is called after the objective function returns and right before the trial is finished and its state is stored.

Note

Added in v2.4.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v2.4.0.

Parameters:

• study (Study) – Target study object.

• trial (FrozenTrial) – Target trial object. Take a copy before modifying this object.

• state (TrialState) – Resulting trial state.

• values (Sequence[float] | None) – Resulting trial values. Guaranteed to not be None if trial succeeded.

Return type:

None

before_trial(study, trial)

Trial pre-processing.

This method is called before the objective function is called and right after the trial is instantiated. More precisely, this method is called during trial initialization, just before the infer_relative_search_space() call. In other words, it is responsible for pre-processing that should be done before inferring the search space.

Note

Added in v3.3.0 as an experimental feature. The interface may change in newer versions without prior notice. See https://github.com/optuna/optuna/releases/tag/v3.3.0.

Parameters:

• study (Study) – Target study object.

• trial (FrozenTrial) – Target trial object.

Return type:

None

infer_relative_search_space(study, trial)

Infer the search space that will be used by relative sampling in the target trial.

This method is called right before sample_relative() method, and the search space returned by this method is passed to it. The parameters not contained in the search space will be sampled by using sample_independent() method.

Parameters:

• study (Study) – Target study object.

• trial (FrozenTrial) – Target trial object. Take a copy before modifying this object.

Returns:

A dictionary containing the parameter names and parameter’s distributions.

Return type:

dict[str, BaseDistribution]

See also

Please refer to intersection_search_space() as an implementation of infer_relative_search_space().

reseed_rng()

Reseed sampler’s random number generator.

This method is called by the Study instance if trials are executed in parallel with the option n_jobs>1. In that case, the sampler instance will be replicated including the state of the random number generator, and they may suggest the same values. To prevent this issue, this method assigns a different seed to each random number generator.

Return type:

None

sample_independent(study, trial, param_name, param_distribution)

Sample a parameter for a given distribution.

This method is called only for the parameters not contained in the search space returned by sample_relative() method. This method is suitable for sampling algorithms that do not use relationship between parameters such as random sampling and TPE.

Note

The failed trials are ignored by any build-in samplers when they sample new parameters. Thus, failed trials are regarded as deleted in the samplers’ perspective.

Parameters:

• study (Study) – Target study object.

• trial (FrozenTrial) – Target trial object. Take a copy before modifying this object.

• param_name (str) – Name of the sampled parameter.

• param_distribution (BaseDistribution) – Distribution object that specifies a prior and/or scale of the sampling algorithm.

Returns:

A parameter value.

Return type:

Any

sample_relative(study, trial, search_space)

Sample parameters in a given search space.

This method is called once at the beginning of each trial, i.e., right before the evaluation of the objective function. This method is suitable for sampling algorithms that use relationship between parameters such as Gaussian Process and CMA-ES.

Note

The failed trials are ignored by any build-in samplers when they sample new parameters. Thus, failed trials are regarded as deleted in the samplers’ perspective.

Parameters:

• study (Study) – Target study object.

• trial (FrozenTrial) – Target trial object. Take a copy before modifying this object.

• search_space (dict[str, BaseDistribution]) – The search space returned by infer_relative_search_space().

Returns:

A dictionary containing the parameter names and the values.

Return type:

dict[str, Any]