Tuning the hyper-parameters of CMA-ES with tree-structured Parzen estimators

CMA-ES is widely used for non-linear and non-convex function optimization, but tuning the hyper-parameters of CMA-ES is a practical challenge. There are three hyper-parameters c_c, c₁ and c_μ of CMA-ES, and it is important for the covariance matrix updates to configure their values. Based on the constraints among c_c, ci and c_μ, we design a tree-structured graph to describe their relationships. We maximize Expected Improvement (EI) to search the configuration space of c_c, c₁ and c_μ, which is based on the distribution of solution quality and the conditional distribution of configuration given solution quality. The two distributions are modeled by the Tree-structured Parzen Estimators (TPE). We evaluate our approach on the BBOB noiseless problems. The experimental results show that our approach mostly gets a faster convergence towards the optimal solutions when compared with the default CMA-ES and the state-of-the-art algorithm self-CMA-ES.