Input Perturbations for Adaptive Control and Learning
This work addresses adaptive control and learning for MIMO systems, offering practical policies with theoretical guarantees, but it appears incremental as it builds on existing methods like self-normalized martingales.
The paper tackles the problem of simultaneous control and learning in MIMO linear dynamical systems by proposing input perturbation-based policies, achieving worst-case regret scaling as the square-root of the time horizon and, in specific settings, logarithmic regret matching the information-theoretic lower bound.
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.