Numerical Evaluation of Exact Person-by-Person Optimal Nonlinear Control Strategies of the Witsenhausen Counterexample

摘要

The Witsenhausen's counterexmaple formulated in 1968 is a decentralized stochastic control problem that highlights the importance of information structure in a seemingly simple two player team problem. Despite immense attention towards the problem, the non-classical information structure therein had remained the key challenge to obtain the optimal solution until recently (2014), when the Person-by-Person nonlinear optimal laws that satisfy integral equations were derived using Girsanov's transformation. In this paper, we compute and implement the nonlinear optimal laws using the Gauss Hermite Quadrature to approximate the integrals and then solving a system of non-linear equations to compute the signaling levels. We then analyse and compare our results with costs previously reported in the literature.