Analyzing the (1, ) Evolution Strategy via Stochastic Approximation Methods

The main objective of this paper is to analyze the (1, ) evolution strategy by use of stochastic approximation methods. Both constant and decreasing step size algorithms are studied. Convergence and estimation error bounds for the (1, ) evolution strategy are developed. First the algorithm is converted to a recursively defined scheme of stochastic approximation type. Then the analysis is carried out by using the analytic tools from stochastic approximation. In lieu of examining the discrete iterates, suitably scaled sequences are defined. These interpolated sequences are then studied in detail. It is shown that the limits of the sequences have natural connections to certain continuous time dynamical systems.

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