Gaussian Adaptation Revisited - An Entropic View on Covariance Matrix Adaptation

We revisit Gaussian Adaptation (GaA), a black-box optimizer for discrete and continuous problems that has been developed in the late 1960’s. This largely neglected search heuristic shares several interesting features with the wellknown Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and with Simulated Annealing (SA). GaA samples single candidate solutions from a multivariate normal distribution and continuously adapts its first and second moments (mean and covariance) such as to maximize the entropy of the search distribution. Sample-point selection is controlled by a monotonically decreasing acceptance threshold, reminiscent of the cooling schedule in SA. We describe the theoretical foundations of GaA and analyze some key features of this algorithm. We empirically show that GaA converges log-linearly on the sphere function and analyze its behavior on selected non-convex test functions.