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Decentralized stochastic control (DSC) considers the optimal control problemof a multi-agent system. However, DSC cannot be solved except in the specialcases because the estimation among the agents is generally intractable. In thiswork, we propose memory-limited DSC (ML-DSC), in which each agent compressesthe observation history into the finite-dimensional memory. Because thiscompression simplifies the estimation among the agents, ML-DSC can be solved inmore general cases based on the mean-field control theory. We demonstrateML-DSC in the general LQG problem. Because estimation and control are notclearly separated in the general LQG problem, the Riccati equation is modifiedto the decentralized Riccati equation, which improves estimation as well ascontrol. Our numerical experiment shows that the decentralized Riccati equationis superior to the conventional Riccati equation.

Mean-Field Control Approach to Decentralized Stochastic Control with Finite-Dimensional Memories