Private & Common Information States for Dynamic Programming of POMDPs With Delayed Sharing Patterns

ISS Informal Systems Seminar
Private and Common Information States for Dynamic Programming of POMDPs With Delayed Sharing Patterns
Charalambos D. Charalambous – University of Cyprus, Cyprus
May 8, 2026

The interest to develop a dynamic programming (DP) approach for multiagent decentralized stochastic optimal control, with delayed sharing information patterns, was initiated in the early 1970's, with the appearance of Witsenhausen's 1971 seminal paper on separation of estimation and control. Most previous studies focused on a single value function (and corresponding DP equation), conditioned on the shared or common information of all controls or agents.

In this talk, I will present a new generalized DP framework based on decentralized team equilibrium called Person-by-Person (PbP) optimality in static team theory. Each agent is assigned an individual value function conditioned on the agent's delayed sharing information pattern, while all other agents' strategies are fixed.

I will introduce several new DP equations which characterize decentralized team equilibrium, with emphasis on the role of private and common information components of each agent's information pattern to reduce complexity and to retain the key fundamental properties of centralized DP equations of partially observable Markov decision problems (POMDPs):

1) the optimization is over the agent's action spaces rather than their strategy spaces,
2) each agent compresses the data into a private information state, and
3) a centralized information state which is common to all agents.

The new DP framework quantifies a conceptual property of optimal strategies to compress their data, initially envisioned by H. Witsenhausen in his paper, "Separation of estimation and control for discrete time systems," in Proceedings of the IEEE, vol. 59, no. 11, pp. 1557-1566, 1971.

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