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.

Strongly Adaptive OCO with Memory