Abstract

CMA-ES is one of the most popular stochastic search algorithms.
It performs favourably in many tasks without the need of extensive
parameter tuning. The algorithm has many beneficial properties,
including automatic step-size adaptation, efficient covariance updates
that incorporates the current samples as well as the evolution
path and its invariance properties. Its update rules are composed
of well established heuristics where the theoretical foundations of
some of these rules are also well understood. In this paper we
will fully derive all CMA-ES update rules within the framework of
expectation-maximisation-based stochastic search algorithms using
information-geometric trust regions. We show that the use of the trust
region results in similar updates to CMA-ES for the mean and the
covariance matrix while it allows for the derivation of an improved
update rule for the step-size. Our new algorithm, Trust-Region Covariance
Matrix Adaptation Evolution Strategy (TR-CMA-ES) is
fully derived from first order optimization principles and performs
favourably in compare to standard CMA-ES algorithm.