Tracking Adversarial Targets

We study linear control problems with quadratic losses and adversarially chosen tracking targets. We present an efficient algorithm for this problem and show that, under standard conditions on the linear system, its regret with respect to an optimal linear policy grows as O(\log^2 T), where T is the number of rounds of the game. We also study a problem with adversarially chosen transition dynamics; we present an exponentially-weighted average algorithm for this problem, and we give regret bounds that grow as O(\sqrt T).