Optimistic Online Non-stochastic Control via FTRL
This work addresses the challenge of using untrusted predictions in online control, advancing the non-stochastic control framework for robust learning-based controllers.
The paper tackles the problem of incorporating predictions of unknown quality into online non-stochastic control, resulting in the first Disturbance Action Controller with optimistic policy regret bounds that range from O(1) for perfect predictions to O(sqrt(T)) for failed ones.
This paper brings the concept of ``optimism" to the new and promising framework of online Non-stochastic Control (NSC). Namely, we study how NSC can benefit from a prediction oracle of unknown quality responsible for forecasting future costs. The posed problem is first reduced to an optimistic learning with delayed feedback problem, which is handled through the Optimistic Follow the Regularized Leader (OFTRL) algorithmic family. This reduction enables the design of \texttt{OptFTRL-C}, the first Disturbance Action Controller (DAC) with optimistic policy regret bounds. These new bounds are commensurate with the oracle's accuracy, ranging from $\mathcal{O}(1)$ for perfect predictions to the order-optimal $\mathcal{O}(\sqrt{T})$ even when all predictions fail. By addressing the challenge of incorporating untrusted predictions into online control, this work contributes to the advancement of the NSC framework and paves the way toward effective and robust learning-based controllers.