Adversarial Tracking Control via Strongly Adaptive Online Learning with Memory
This work provides a new adversarial tracking controller with strong performance guarantees for linear dynamical systems, which is relevant for control engineers dealing with unpredictable environments.
This paper addresses the problem of tracking an adversarial state sequence in a linear dynamical system with adversarial disturbances and loss functions. It introduces a comparator-adaptive algorithm for online linear optimization with movement cost, a strongly adaptive algorithm for online learning with memory, and a reduction from adversarial tracking control to strongly adaptive online learning with memory, resulting in a controller with strong performance guarantees.
We consider the problem of tracking an adversarial state sequence in a linear dynamical system subject to adversarial disturbances and loss functions, generalizing earlier settings in the literature. To this end, we develop three techniques, each of independent interest. First, we propose a comparator-adaptive algorithm for online linear optimization with movement cost. Without tuning, it nearly matches the performance of the optimally tuned gradient descent in hindsight. Next, considering a related problem called online learning with memory, we construct a novel strongly adaptive algorithm that uses our first contribution as a building block. Finally, we present the first reduction from adversarial tracking control to strongly adaptive online learning with memory. Summarizing these individual techniques, we obtain an adversarial tracking controller with a strong performance guarantee even when the reference trajectory has a large range of movement.