Meta-Learning Online Control for Linear Dynamical Systems

• 成果类型: Article
• 署名作者: Muthirayan, Deepan; Kalathil, Dileep; Khargonekar, Pramod P.
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3536839
• 发表日期: 2025
• 页码: 4163-4169
• 关键词: Metalearning; Heuristic algorithms; cost function; dynamical systems; COSTS; STANDARDS; noise; system dynamics; robots; Machine learning algorithms; Linear systems control; meta-learning; online control

摘要

In this article, we consider the problem of finding a meta-learning online control algorithm that can learn across the tasks when faced with a sequence of N (similar) control tasks. Each task involves controlling a linear dynamical system for a finite horizon of T time steps. The cost function and system noise at each time step are adversarial and unknown to the controller before taking the control action. Meta-learning is a broad approach where the goal is to prescribe an online policy for any new unseen task exploiting the information from other tasks and the similarity between the tasks. We propose a meta-learning online control algorithm for the control setting and characterize its performance by meta-regret, the average cumulative regret across the tasks. We show that when the number of tasks are sufficiently large, our proposed approach achieves a meta-regret that is smaller by a factor D/D-& lowast; compared to an independent-learning online control algorithm, which does not perform learning across the tasks, where D is a problem constant and D-& lowast; is a scalar that decreases with increase in the similarity between tasks. Thus, when the sequence of tasks are similar the regret of the proposed meta-learning online control is significantly lower than that of the naive approaches without meta-learning. We also present experiment results to demonstrate the superior performance achieved by our meta-learning algorithm.