Maximum Entropy Optimal Density Control of Discrete-Time Linear Systems and Schrodinger Bridges

• 成果类型: Article
• 署名作者: Ito, Kaito; Kashima, Kenji
• 署名单位: Institute of Science Tokyo; Tokyo Institute of Technology; Kyoto University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3305319
• 发表日期: 2024
• 页码: 1536-1551
• 关键词: Maximum entropy (MaxEnt); optimal control; Schrödinger Bridge; stochastic control

摘要

We consider an entropy-regularized version of optimal density control of deterministic discrete-time linear systems. Entropy regularization, or a maximum entropy (MaxEnt) method for optimal control, has attracted much attention especially in reinforcement learning due to its many advantages, such as a natural exploration strategy. Despite the merits, high-entropy control policies induced by the regularization introduce probabilistic uncertainty into systems, which severely limits the applicability of MaxEnt optimal control to safety-critical systems. To remedy this situation, we impose a Gaussian density constraint at a specified time on the MaxEnt optimal control to directly control state uncertainty. Specifically, we derive the explicit form of the MaxEnt optimal density control. In addition, we also consider the case where density constraints are replaced by fixed-point constraints. Then, we characterize the associated state process as a pinned process, which is a generalization of the Brownian bridge to linear systems. Finally, we reveal that the MaxEnt optimal density control gives the so-called Schrodinger bridge associated with a discrete-time linear system.