Simplified dynamic programming for Decentralized POMDPs with delayed sharing Information patterns via change of measure

In this paper, we consider decentralized discretetime stochastic dynamical optimal control problems with multiple control strategies operating under delayed-sharing information

patterns, formulated within the framework of personby-person (PbP) optimality. We invoke Girsanov’s theorem to characterize PbP optimality under a reference probability

measure through value functions satisfying simplified dynamic programming (DP) equations, together with corresponding information states that serve as sufficient statistics for the strategies. The value functions and information states retain the fundamental properties of classical partially observable Markov decision problems (POMDPs), namely, both depend on the actions of the minimizing controls, rather than their strategies.

The main distinguishing feature of our DP approach is that each control strategy estimates the unobservable state process and the private information components of all other strategies solely from its own private information and the delayed-sharing information components, using information states.