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Mutual Information Optimal Density Control of Linear Systems and Generalized Schr"odinger Bridges with Reference Refinement

arXiv 2605.09349 ↗First posted 10 May 2026math.OC cs.LG cs.SYcited by 0

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Abstract (arXiv)

We consider a mutual information (MI) regularized optimal density control of a discrete-time linear system. MI optimal control has been utilized for exploration in reinforcement learning and privacy protection in control. MI regularization induces stochasticity in the policy, which poses challenges for applications of MI optimal control in safety-critical scenarios. To remedy this situation, we impose Gaussian density constraints at specified times to directly control state uncertainty. For this MI optimal density control problem, we propose an alternating optimization algorithm and investigate its convergence properties. In addition, we reveal a relationship between the MI optimal density control problem and a so-called generalized Schr"odinger bridge problem associated with the discrete-time linear system. Based on the results of MI optimal density control and this relationship, we also investigate alternating optimization for the Schr"odinger bridge problem and its convergence properties.

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References · 23

  1. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,885
  2. 2021Convex optimizationcited by 2,515
  3. 2017Reinforcement Learning with Deep Energy-Based Policiescited by 669
  4. 2018Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Reviewcited by 482
  5. 2018Provably Efficient Maximum Entropy Explorationcited by 242
  6. 2021Maximum Entropy RL (Provably) Solves Some Robust RL Problemscited by 176
  7. 2014On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpointcited by 99
  8. 2019Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Driftcited by 50
  9. 2024Multi-marginal Schr"odinger Bridges with Iterative Reference Refinementcited by 27
  10. 2014Optimal steering of a linear stochastic system to a final probability distributioncited by 22
  11. 2019Mutual-Information Regularization in Markov Decision Processes and Actor-Critic Learningcited by 18
  12. 2021Density control of interacting agent systemscited by 13
11 more
  1. 2018Optimal Covariance Control for Stochastic Systems Under Chance Constraintscited by 7
  2. 2019Nonlinear Covariance Control via Differential Dynamic Programmingcited by 6
  3. 2020Deep RL With Information Constrained Policies: Generalization in Continuous Controlcited by 6
  4. 2020Privacy-Constrained Policies via Mutual Information Regularized Policy Gradientscited by 6
  5. 2022Maximum entropy optimal density control of discrete-time linear systems and Schr"odinger bridgescited by 6
  6. 2023Maximum Entropy Density Control of Discrete-Time Linear Systems with Quadratic Costcited by 6
  7. 2018Optimal Transport over Deterministic Discrete-time Nonlinear Systems using Stochastic Feedback Lawscited by 4
  8. 2024Reachability and Controllability Analysis of the State Covariance for Linear Stochastic Systemscited by 3
  9. 2022Optimal Covariance Steering for Discrete-Time Linear Stochastic Systemscited by 2
  10. 2025Mutual Information Optimal Control of Discrete-Time Linear Systemscited by 2
  11. 2025On Policy Stochasticity in Mutual Information Optimal Control of Linear Systemscited by 1

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