Learning approaches to the Witsenhausen counterexample from a view of potential games

Abstract

Abstract-Since Witsenhausen put forward his remarkable counterexample in 1968, there have been many attempts to develop efficient methods for solving this non-convex functional optimization problem. However there are few methods designed from game theoretic perspectives. In this paper, after discretizing the Witsenhausen counterexample and re-writing the formulation in analytical expressions, we use fading memory JSFP with inertia, one learning approach in games, to search for better controllers from a view of potential games. We achieve a better solution than the previously known best one. Moreover, we show that the learning approaches are simple and automated and they are easy to extend for solving general functional optimization problems.

Iterative source-channel coding approach to Witsenhausen's counterexample

“…For ease of comparison, we have also included the costs of previously reported results. As can be seen, all our mappings have similar performance and all of them give lower costs than the previously reported lowest cost -0.1670790 [17].…”

On information structures, convexity, and linear optimality

“…(iv) is fairly open-ended as well, and there has certainly been a progression of nonlinear optimization theory and tools, but there have also been specific efforts to approach the optimal solution for the Witsenhausen counterexample, or to use it as a testbed for new optimization tools. In particular, the best known achievable cost (for benchmark values of the parameters) was driven to a new low in [3] and was further improved upon in [4].…”

Witsenhausen's counterexample: A view from optimal transport theory

“…As illustrated in Fig. 1, Witsenhausen's counterexample is a two-stage decentralized stochastic control problem, where the goal is to minimize the weighted average control cost k 2 E U Numerical algorithms that provide upper bounds on the optimal cost have been proposed using neural networks [6], hierarchical search [7], learning approach [8], etc. Based on information-theoretical ideas, [9], [10] developed upper and lower bounds that are within a constant factor using lattice quantization and joint-source-channel coding converse respectively.…”