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), c(1) and c(mu) of CMA-ES, and it is important for the covariance matrix updates to configure their values. Based on the constraints among c(c), c(1) and c(mu), we design a tree structured graph to describe their relationships. We maximize Expected Improvement (El) to search the configuration space of c(c), c(1) and c(mu), 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.