# Mutual Information Optimal Control of Discrete-Time Linear Systems

arXiv: https://arxiv.org/abs/2507.04712 · HTML: https://mlsanity.com/paper/2507.04712/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 15 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [Mutual-Information Regularization in Markov Decision Processes and Actor-Critic Learning](https://mlsanity.com/paper/1909.05950/) (2019)
- [LQG Control with Minimum Directed Information: Semidefinite Programming Approach](https://mlsanity.com/paper/1510.04214/) (2015)
- [Maximum entropy optimal density control of discrete-time linear systems and Schr"odinger bridges](https://mlsanity.com/paper/2204.05263/) (2022)
- [Maximum Entropy Density Control of Discrete-Time Linear Systems with Quadratic Cost](https://mlsanity.com/paper/2309.10662/) (2023)
- [Maximum Entropy Differential Dynamic Programming](https://mlsanity.com/paper/2110.06451/) (2021)

## Built on by (most cited first, 2 of 2)

- [On Policy Stochasticity in Mutual Information Optimal Control of Linear Systems](https://mlsanity.com/paper/2507.21543/) (2025)
- [Mutual Information Optimal Density Control of Linear Systems and Generalized Schr"odinger Bridges with Reference Refinement](https://mlsanity.com/paper/2605.09349/) (2026)

## Abstract (arXiv)

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.