Mutual Information Optimal Control of Discrete-Time Linear Systems

TL;DR

This paper introduces a mutual information optimal control framework for discrete-time linear systems, optimizing policy and prior jointly, with analytical solutions and an iterative algorithm demonstrated through numerical experiments.

Contribution

It extends maximum entropy optimal control by jointly optimizing policy and prior, providing analytical solutions and an iterative algorithm for discrete-time linear systems.

Findings

Derived optimal policy and prior under Gaussian assumptions

Proposed an alternating minimization algorithm

Validated effectiveness through numerical experiments

Abstract

In this paper, we formulate a mutual information optimal control problem (MIOCP) for discrete-time linear systems. This problem can be regarded as an extension of a maximum entropy optimal control problem (MEOCP). Differently from the MEOCP where the prior is fixed to the uniform distribution, the MIOCP optimizes the policy and prior simultaneously. As analytical results, under the policy and prior classes consisting of Gaussian distributions, we derive the optimal policy and prior of the MIOCP with the prior and policy fixed, respectively. Using the results, we propose an alternating minimization algorithm for the MIOCP. Through numerical experiments, we discuss how our proposed algorithm works.