具有动态批长度和自适应学习率的在线赌博机非线性控制
Online Bandit Nonlinear Control with Dynamic Batch Length and Adaptive Learning Rate
AI总结：
本文提出DBAR算法，通过动态批长度和自适应学习率，在仅需弱稳定性概念且无指数稳定控制器的条件下，实现非线性系统在线赌博机控制的渐近稳定与紧遗憾界。
摘要：
本文研究在线赌博机非线性控制问题，其目标是从一个包含未知类型的稳定与不稳定控制器的控制器池中，为给定的非线性动态系统学习最优的稳定控制器。我们提出了一种名为动态批长度与自适应学习率（DBAR）的算法，并研究了其稳定性与遗憾界。与现有需要指数稳定控制器的Exp3算法不同，DBAR只需要一种显著更弱的控制器稳定性概念，在这种情况下，认证系统稳定性可能需要大量时间。DBAR中的动态批长度有效解决了这一问题，使系统能够达到渐近稳定，此时算法的表现如同不存在不稳定控制器一样。此外，DBAR中的自适应学习率仅利用状态范数信息即可实现紧的遗憾界，即使控制器池中没有任何稳定控制器是指数稳定的。
英文摘要：
This paper is concerned with the online bandit nonlinear control, which aims to learn the best stabilizing controller from a pool of stabilizing and destabilizing controllers of unknown types for a given nonlinear dynamical system. We develop an algorithm, named Dynamic Batch length and Adaptive learning Rate (DBAR), and study its stability and regret. Unlike the existing Exp3 algorithm requiring an exponentially stabilizing controller, DBAR only needs a significantly weaker notion of controller stability, in which case substantial time may be required to certify the system stability. Dynamic batch length in DBAR effectively addresses this issue and enables the system to attain asymptotic stability, where the algorithm behaves as if there were no destabilizing controllers. Moreover, adaptive learning rate in DBAR only uses the state norm information to achieve a tight regret bound even when none of the stabilizing controllers in the pool are exponentially stabilizing.
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