On the Guarantees of Minimizing Regret in Receding Horizon

• 成果类型: Article
• 署名作者: Martin, Andrea; Furieri, Luca; Dorfler, Florian; Lygeros, John; Ferrari-Trecate, Giancarlo
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3464013
• 发表日期: 2025
• 页码: 1547-1562
• 关键词: safety; PLANNING; optimization; infinite horizon; Heuristic algorithms; COSTS; Benchmark testing; Constrained control; optimal control; predictive control for linear systems; regret-optimal control; stability of linear systems

摘要

Toward bridging classical optimal control and online learning, regret minimization has recently been proposed as a control design criterion. This competitive paradigm penalizes the loss relative to the optimal control actions chosen by a clairvoyant policy, and allows tracking the optimal performance in hindsight no matter how disturbances are generated. In this article, we propose the first receding horizon scheme based on the repeated computation of finite horizon regret-optimal policies, and we establish stability and safety guarantees for the resulting closed-loop system. Our derivations combine novel monotonicity properties of clairvoyant policies with suitable terminal ingredients. We prove that our scheme is recursively feasible, stabilizing, and that it achieves bounded regret relative to the infinite horizon clairvoyant policy. Last, we show that the policy optimization problem can be solved efficiently through convex-concave programming. Our numerical experiments show that minimizing regret can outperform standard receding horizon approaches when the disturbances poorly fit classical design assumptions-even when the finite horizon planning is recomputed less frequently.