Deterministic Annealing Optimization for Witsenhausen's and Related Decentralized Stochastic Control Problems

Abstract: This note studies the global optimization of controller mappings in discrete-time stochastic control problems including Witsenhausen's celebrated 1968 counter-example. We propose a generally applicable non-convex numerical optimization method based on the concept of deterministic annealing-which is derived from information-theoretic principles and was successfully employed in several problems including vector quantization, classification, and regression. We present comparative numerical results for two test problems that show the strict superiority of the proposed method over prior approaches in the literature.