Input perturbations for adaptive control and learning. (July 2020)

• Record Type: Journal Article
• Authors: Shirani Faradonbeh, Mohamad Kazem; Tewari, Ambuj; Michailidis, George
• Is Part Of: Automatica. Volume 117(2020)
• Publication Date: 2020-07
• Subjects: Finite-time optimality -- Greedy policies -- Adaptive LQRs -- System identification -- Decision-making under uncertainty -- Linear–quadratic -- Exploration–exploitation; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.108950
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper studies adaptive algorithms for simultaneous regulation (i.e., control) and estimation (i.e., learning) of Multiple Input Multiple Output (MIMO) linear dynamical systems. It proposes practical, easy to implement control policies based on perturbations of input signals. Such policies are shown to achieve a worst-case regret that scales as the square-root of the time horizon, and holds uniformly over time. Further, it discusses specific settings where such greedy policies attain the information theoretic lower bound of logarithmic regret. To establish the results, recent advances on self-normalized martingales together with a novel method of policy decomposition are leveraged.