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.

本文研究了多输入多输出线性动态系统的同时调节和估计的自适应算法，提出了基于输入信号扰动的实用、易于实现的控制策略，这些策略表现出随着时间的平方根成比例恶劣后果，并且在时间上均匀保持。进一步讨论了特定的设置，其中这些贪婪策略达到了对数后悔的信息理论下界。为了证明这些结果，运用了最近关于自标准化鞅和策略分解的新方法。

适应性控制和学习的输入扰动

Input Perturbations for Adaptive Control and Learning

We propose several exponential inequalities for self-normalized martingales
similar to those established by De la Pe\~{n}a. The keystone is the
introduction of a new notion of random variable heavy on left or right.
Applications associated with linear regressions, autoregressive and branching
processes are also provided.

提出了几个类似于 De la Peña 建立的自标准化鞅的指数不等式，其中关键是引入了左重右重的新随机变量概念，并提供了与线性回归，自回归和分支过程相关的应用。