Memory-Limited Partially Observable Stochastic Control and its Mean-Field Control Approach

TL;DR

This paper introduces ML-POSC, a new framework for control problems with incomplete information and memory limits, utilizing mean-field control theory to enable practical solutions and generalize classical problems like LQG.

Contribution

The paper proposes ML-POSC, an innovative framework that incorporates memory limitations into partially observable stochastic control and employs mean-field control techniques for practical solvability.

Findings

ML-POSC generalizes LQG to include memory constraints.

Modified Riccati equation improves estimation and control.

ML-POSC outperforms local LQG approximation in non-LQG scenarios.

Abstract

Control problems with incomplete information and memory limitation appear in many practical situations. Although partially observable stochastic control (POSC) is a conventional theoretical framework that considers the optimal control problem with incomplete information, it cannot consider memory limitation. Furthermore, POSC cannot be solved in practice except in the special cases. In order to address these issues, we propose an alternative theoretical framework, memory-limited POSC (ML-POSC). ML-POSC directly considers memory limitation as well as incomplete information, and it can be solved in practice by employing the mathematical technique of the mean-field control theory. ML-POSC can generalize the LQG problem to include memory limitation. Because estimation and control are not clearly separated in the LQG problem with memory limitation, the Riccati equation is modified to the partially observable Riccati equation, which improves estimation as well as control. Furthermore, we demonstrate the effectiveness of ML-POSC to a non-LQG problem by comparing it with the local LQG approximation.