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.

本文研究了用于多输入多输出（MIMO）线性动力系统的同时调节（即控制）和估计（即学习）的自适应算法。它提出了一种实用，易于实施的基于输入信号扰动的控制策略。事实证明，此类政策会产生最坏的遗憾，这种遗憾会随着时间跨度的平方根而变，并且随着时间的推移而统一。此外，它讨论了具体的设置，在这些设置中，这种贪婪策略达到了对数后悔的信息理论下限。为了建立结果，利用了自归一化mar的最新进展以及一种新的政策分解方法。