  Recent progress in online control has popularized online learning with
memory, a variant of the standard online learning problem with loss functions
dependent on the prediction history. In this paper, we propose the first
strongly adaptive algorithm for this problem: on any interval
$\mathcal{I}\subset[1:T]$, the proposed algorithm achieves $\tilde
O\left(\sqrt{|\mathcal{I}|}\right)$ policy regret against the best fixed
comparator for that interval. Combined with online control techniques, our
algorithm results in a strongly adaptive regret bound for the control of linear
time-varying systems.
