  We consider the problem of online control of systems with time-varying linear
dynamics. This is a general formulation that is motivated by the use of local
linearization in control of nonlinear dynamical systems. To state meaningful
guarantees over changing environments, we introduce the metric of {\it 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 {\it 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 {\it adaptive
regret} bounds in the setting of time-varying linear dynamical systems. The
main 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.
