This paper brings the concept of "optimism" to the new and promising
framework of online Non-stochastic Control (NSC). Namely, we study how can NSC
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 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 control
systems, our work contributes to the advancement of the NSC framework and paves
the way towards effective and robust learning-based controllers.

该研究论文将 “乐观主义” 概念引入在线非随机控制（NSC）的新颖框架中，研究了如何利用负责预测未来成本的未知质量的预测预报器使 NSC 受益。首先将问题简化为具有延迟反馈的乐观学习问题，并通过乐观正则化领导者（OFTRL）算法家族来解决。这种简化使得设计 OptFTRL-C 成为第一个拥有乐观策略遗憾界限的干扰行为控制器（DAC）。这些新界限与预测预报器的准确性成正比，从完美预测的 Ο(1) 到当所有预测失败时的算法最优 Ο(T^0.5)。通过解决将不可信预测纳入控制系统的挑战，该研究工作在 NSC 框架的推进以及实现有效和稳健的学习控制器方面做出了贡献。