Computing optimal control laws for finite stochastic systems with non-classical information patterns

Computation of optimal control laws for systems with non-classical information patterns and its relation to signaling is still an open problem. The notion of information states redefines such optimal control problems as centralized problems on arbitrary function spaces. We propose a method to transform the resulting functional optimization problem into a multi-parametric mixed-integer program. While the underlying problem remains intractable for large-scale systems, our contribution allows to compute optimal decentralized control laws for limited size problems in a systematic fashion and reveals a signaling structure for decentralized systems. We illustrate the proposed technique by computing optimal control laws for a discrete-time finite-space formulation of the system used in the Witsenhausen counterexample. Numerical results show that the tuple of optimal control laws acts as a communication system (an n-bit quantizer followed by a ML-decoder).