Information Structures, the Witsenhausen Counterexample, and Communicating Using Actions

The concept of “information-structures” in decentralized control is a formalization of the notion of “who knows what and when do they know it.” Even seemingly simple problems with simply stated information structures can be extremely hard to solve. Perhaps the simplest of such unsolved problem is the celebrated Witsenhausen counterexample, formulated by Hans Witsenhausen in 1968. This article discusses how the information structure of the Witsenhausen counterexample makes it hard, and how an information-theoretic approach, that explores the knowledge-gradient due to a non-classical information pattern, has helped obtain insights into the problem.