Beyond No-Regret: Competitive Control via Online Optimization with Memory
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This paper studies online control with adversarial disturbances using tools from online optimization with memory. Most work that bridges learning and control theory focuses on designing policies that are no-regret with respect to the best static linear controller in hindsight. However, the optimal offline controller can have orders-of-magnitude lower cost than the best linear controller. We instead focus on achieving constant competitive ratio compared to the offline optimal controller, which need not be linear or static. We provide a novel reduction from online control of a class of controllable systems to online convex optimization with memory. We then design a new algorithm for online convex optimization with memory, Optimistic Regularized Online Balanced Descent, that has a constant, dimension-free competitive ratio. This result, in turn, leads to a new constant-competitive approach for online control.
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