MAPCMA sampler

Abstract

MAPCMASampler provides an implementation of the MAP-IGO (maximum a posteriori information geometric optimization) framework, which extends the CMA-ES rank-one-update. This sampler adds momentum-based updates to the standard CMA-ES, following the MAP-IGO algorithm.

Class or Function Names

• MAPCMASampler(mean: dict[str, Any] | None = None, sigma0: float | None = None, seed: int | None = None, popsize: int | None = None, cov: np.ndarray | None = None, momentum_r: float | None = None, search_space: dict[str, BaseDistribution] | None = None, independent_sampler: BaseSampler | None = None)
  • mean: Initial mean of MAPCMA. If not provided, the mean will be set to the center of the search space.
  • sigma0: The initial standard deviation of covariance matrix. If not provided, it will be set based on the search space bounds.
  • seed: The seed of the random number generator.
  • popsize: The population size. If not provided, the population size will be set based on the search space dimensionality (4 + floor(3 * log(dimension))).
  • cov: The initial covariance matrix. If not provided, it will be set to the identity matrix scaled by sigma0.
  • momentum_r: Scaling ratio of momentum update. This parameter controls the momentum-based update in the MAP-IGO framework.
  • search_space: A dictionary containing the search space that defines the parameter space. The keys are the parameter names and the values are the parameter’s distribution. If the search space is not provided, the sampler will infer the search space dynamically during the first trial.
  • independent_sampler: A :class:~optuna.samplers.BaseSampler instance that is used for independent sampling. The parameters not contained in the relative search space are sampled by this sampler. If :obj:None is specified, :class:~optuna.samplers.RandomSampler is used as the default.

Note that because of the limitation of the algorithm, only non-conditional numerical parameters can be sampled by the MAPCMA algorithm, and categorical and conditional parameters are handled by the independent sampler.

Installation

pip install -r https://hub.optuna.org/samplers/mapcma/requirements.txt

Example

from __future__ import annotations

import optuna
import optunahub


def objective(trial: optuna.Trial) -> float:
    x = trial.suggest_float("x", -5, 5)
    y = trial.suggest_float("y", -5, 5)
    return x**2 + y**2


if __name__ == "__main__":
    sampler = optunahub.load_module(
        package="samplers/mapcma",
    ).MAPCMASampler()

    study = optuna.create_study(sampler=sampler)
    study.optimize(objective, n_trials=100)
    print(study.best_params)

Reference

Hamano, Ryoki, Shinichi Shirakawa, and Masahiro Nomura. “Natural Gradient Interpretation of Rank-One Update in CMA-ES.” International Conference on Parallel Problem Solving from Nature. Cham: Springer Nature Switzerland, 2024.

BibTex

@inproceedings{hamano2024natural,
  title={Natural Gradient Interpretation of Rank-One Update in CMA-ES},
  author={Hamano, Ryoki and Shirakawa, Shinichi and Nomura, Masahiro},
  booktitle={International Conference on Parallel Problem Solving from Nature},
  pages={252--267},
  year={2024},
  organization={Springer}
}