Learning Rate Adaptation CMA-ES for Multimodal and Noisy Problems with Low Effective Dimensionality
Haruhito Nakagawa, Yutaro Yamada, Kento Uchida, Shinichi Shirakawa · Proceedings of the Genetic and Evolutionary Computation Conference Companion · 2025
To improve Covariance matrix adaptation evolution strategy (CMA-ES), which needs tuning of hyperparameters for optimizing multimodal and noisy problems, learning rate adaptation CMA-ES (LRA-CMA-ES) was proposed. This method adapts the learning rates based on the signal-to-noise ratio (SNR) of the update directions. On several high-dimensional optimization problems, part of the design variable affects the evaluation value and other variables are redundant. This property is called low effective dimensionality (LED). Although LRA-CMA-ES shows robust performance on multimodal and noisy problems, its performance is deteriorated by LED. To improve the performance on functions with LED, this paper introduces the countermeasures for LED to LRA-CMA-ES. The proposed method, LRA-CMA-ES-LED, estimates the element-wise SNR on the direction along the eigenvector of the covariance matrix to compute the effectiveness of each direction. We reduce the influence of redundant directions on the learning rate adaptation mechanism based on the estimated effectiveness. In the numerical experiments, we used benchmark functions in tens of dimensions containing 10 effective directions, which shows the performance improvement on multimodal and noisy problems with LED.