Adaptive Regret for Control of Time-Varying Dynamics
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We consider regret minimization for online control with time-varying linear dynamical systems. The metric of performance we study is adaptive policy regret, or regret compared to the best policy on any interval in time. We give an efficient algorithm that attains first-order adaptive regret guarantees for the setting of online convex optimization with memory. We also show that these first-order bounds are nearly tight. This algorithm is then used to derive a controller with adaptive regret guarantees that provably competes with the best linear controller on any interval in time. We validate these theoretical findings experimentally on simulations of time-varying dynamics and disturbances.
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