Adaptive Regret for Control of Time-Varying Dynamics

We consider the problem of online control of systems with time-varying linear dynamics. To state meaningful guarantees over changing environments, we introduce the metric of adaptive regret to the field of control. This metric, originally studied in online learning, measures performance in terms of regret against the best policy in hindsight on any interval in time, and thus captures the adaptation of the controller to changing dynamics. Our main contribution is a novel efficient meta-algorithm: it converts a controller with sublinear regret bounds into one with sublinear adaptive regret bounds in the setting of time-varying linear dynamical systems. The underlying technical innovation is the first adaptive regret bound for the more general framework of online convex optimization with memory. Furthermore, we give a lower bound showing that our attained adaptive regret bound is nearly tight for this general framework.