Online Bandit Nonlinear Control with Dynamic Batch Length and Adaptive Learning Rate

Jihun Kim, Javad Lavaei

Keywords: Online nonlinear control, Bandits, Dynamic batch length, Adaptive learning rate

TL;DR: We propose a novel bandit-type algorithm for the online nonstochastic control problem using a dynamic batch length and an adaptive learning rate, operating under a much weaker controller stability assumption than exponentially stabilizing notions.

Abstract: 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.

Primary Area: learning on time series and dynamical systems

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Submission Number: 1215