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

TL;DR

This paper introduces a deterministic annealing-based numerical optimization method for solving complex decentralized stochastic control problems, demonstrating its effectiveness over previous approaches through comparative results.

Contribution

It presents a novel application of deterministic annealing to optimize controller mappings in Witsenhausen's problem and related stochastic control challenges.

Findings

The proposed method outperforms prior approaches in test problems.

Numerical results show improved solutions for Witsenhausen's problem.

The approach is broadly applicable to similar 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.