Iterative Source-Channel Coding Approach to Witsenhausen's Counterexample

TL;DR

This paper presents a simple iterative source-channel coding method to solve Witsenhausen's counterexample, achieving the lowest known cost without assumptions on policy space shape.

Contribution

It introduces a novel iterative approach for Witsenhausen's problem that is simple and makes no assumptions about policy space, improving the minimal cost solution.

Findings

Achieved minimal cost of 0.16692462, the lowest known to date.

Method is simple and assumption-free.

Effective for solving complex nonlinear decision problems.

Abstract

In 1968, Witsenhausen introduced his famous counterexample where he showed that even in the simple linear quadratic static team decision problem, complex nonlinear decisions could outperform any given linear decision. This problem has served as a benchmark problem for decades where researchers try to achieve the optimal solution. This paper introduces a systematic iterative source--channel coding approach to solve problems of the Witsenhausen Counterexample-character. The advantage of the presented approach is its simplicity. Also, no assumptions are made about the shape of the space of policies. The minimal cost obtained using the introduced method is 0.16692462, which is the lowest known to date.