论文标题
自适应线性控制中的速率最佳在线凸优化
Rate-Optimal Online Convex Optimization in Adaptive Linear Control
论文作者
论文摘要
我们考虑控制未知的线性动力系统在对抗变化的凸成本和国家和成本功能的全部反馈下的问题。我们提出了第一种计算算法，该算法与最佳的稳定线性控制器相比，该算法达到了最佳$ \ smash {\ sqrt {t}} $ - 遗憾的速率，同时避免在诸如强凸度之类的成本上避免进行严格的假设。我们的方法是基于对在线成本的仔细设计较低的置信度范围，并使用一种新颖的技术来计算有效的遗憾最小化这些界限，从而利用其特定的非convex结构。
We consider the problem of controlling an unknown linear dynamical system under adversarially changing convex costs and full feedback of both the state and cost function. We present the first computationally-efficient algorithm that attains an optimal $\smash{\sqrt{T}}$-regret rate compared to the best stabilizing linear controller in hindsight, while avoiding stringent assumptions on the costs such as strong convexity. Our approach is based on a careful design of non-convex lower confidence bounds for the online costs, and uses a novel technique for computationally-efficient regret minimization of these bounds that leverages their particular non-convex structure.
