标题： 对抗性在线控制的对数遗憾 显示英文标题

标题： Logarithmic Regret for Adversarial Online Control

摘要： 我们引入了一种新的在线线性二次控制算法，适用于已知系统在对抗性扰动下的情况。 在此设置中，现有的遗憾界为$\sqrt{T}$，除非对扰动过程施加强随机假设。 我们给出了第一个针对任意对抗性扰动序列的算法，前提是状态和控制成本由已知的二次函数给出。 我们的算法和分析使用最优离线控制律的特征，将在线控制问题转化为带有近似优势函数的（延迟）在线学习。 与之前的技术相比，我们的方法不需要控制迭代的移动成本，从而实现了对数遗憾。 显示英文摘要

摘要： We introduce a new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances. Existing regret bounds for this setting scale as $\sqrt{T}$ unless strong stochastic assumptions are imposed on the disturbance process. We give the first algorithm with logarithmic regret for arbitrary adversarial disturbance sequences, provided the state and control costs are given by known quadratic functions. Our algorithm and analysis use a characterization for the optimal offline control law to reduce the online control problem to (delayed) online learning with approximate advantage functions. Compared to previous techniques, our approach does not need to control movement costs for the iterates, leading to logarithmic regret.