  Decentralized stochastic control (DSC) considers the optimal control problem
of a multi-agent system. However, DSC cannot be solved except in the special
cases because the estimation among the agents is generally intractable. In this
work, we propose memory-limited DSC (ML-DSC), in which each agent compresses
the observation history into the finite-dimensional memory. Because this
compression simplifies the estimation among the agents, ML-DSC can be solved in
more general cases based on the mean-field control theory. We demonstrate
ML-DSC in the general LQG problem. Because estimation and control are not
clearly separated in the general LQG problem, the Riccati equation is modified
to the decentralized Riccati equation, which improves estimation as well as
control. Our numerical experiment shows that the decentralized Riccati equation
is superior to the conventional Riccati equation.
