Effect of the mean vector learning rate in CMA-ES
Hidekazu Miyazawa, Youhei Akimoto · Proceedings of the Genetic and Evolutionary Computation Conference · 2017
We investigate the effect of the mean vector learning rate in variants of CMA-ES. The learning rate is set to one in the standard setting, but it is natural to set it to a lower value from the perspective of the CMA-ES as the natural gradient method. Our experiments show that decreasing the mean vector learning rate has an effect similar to increasing the population size in the rank-μ update CMA-ES, and well structured multimodal functions can be solved with the default population size by introducing a small learning rate. On the contrary, the CMA-ES with the cumulative step-size adaptation (CSA) fails to locate the global optimum on well structured multimodal functions with the default population size even if a small learning rate is introduced. The results are discussed from the viewpoint of KL-divergence in relation with the optimal step-size. A parameter setting for the CMA-ES with CSA is reconsidered and evaluated on test problems. The results show the CMA-ES with CSA can solve well structured multimodal functions on dimension up to 80 with high probability with population size of ten if the mean vector learning rate is set small enough.