Sign-Averaging Covariance Matrix Adaptation Evolution Strategy

Daiki Morinaga, Youhei Akimoto

Abstract: In black-box optimization, the user inevitably encounters noise in an objective function. Many noise treatment techniques have been developed to properly evaluate the effectiveness of solutions in the optimization process. A noise treatment called sign averaging was proposed recently, and it is proved that the adverse effects of noise can be reduced and the ranking of the candidate solutions on the median of the objective function can be estimated, even when the mean of the objective function is not well-defined. Although a theoretical guarantee exists, empirical studies on sign averaging are yet to be conducted. In this study, we implemented sign averaging in a covariance matrix adaptation evolution strategy, named the SA-CMA-ES, with an adaptive mechanism controlling the strength of the noise treatment. We experimentally demonstrated that 1) the SA-CMA-ES successfully continues to lower the median of the objective function given more budgets and is more sample efficient than the SA-CMA-ES without the adaptive mechanism for sign averaging; 2) the SA-CMA-ES is competitive with the UH-CMA-ES with Monte-Carlo median estimation and that with conventional averaging for optimizing the mean and median, and it is better than that with conventional averaging when the variance of the objective function is not well-defined.