AI 中文总结
本文围绕线性时不变系统的最优控制问题，综述了多臂老虎机等四大研究方向，提出极小极大最优双重控制器为鲁棒双重控制提供了新的有前景框架。
AI 中文摘要
“双重控制”指的是同时平衡探索与利用的双重目标，这类问题已被研究近一个世纪。本文聚焦于初始参数未知、需通过主动探测学习的线性时不变系统最优控制的理论与方法，综述了四大主要研究方向的核心思想：多臂老虎机、自校正调节器、 regret 率最小化控制器以及极小极大最优双重控制器。前三者历史悠久且文献丰富，而后者为鲁棒双重控制提供了颇具前景的框架。
英文摘要
The term "dual control" refers to the dual objective of simultaneously balancing exploration and exploitation. Problems of this kind have been studied for nearly a century. This paper is devoted to theory and methodology relevant for optimal control of linear time-invariant systems whose parameters are initially unknown and must be learned by active probing. We review the main ideas underlying four major research directions: Multi-armed bandits, self-tuning regulators, regret rate minimizing controllers, and minimax optimal dual controllers. The first three have a long history and rich literature, whereas the fourth provides a promising framework for robust dual control.
CommentsTo be published in Annual Review of Control, Robotics, and Autonomous Systems Vol. 10 (2027)
