在动态遗憾中跟随正则化领导者：乐观与历史修剪
On the Dynamic Regret of Following the Regularized Leader: Optimism with History Pruning
- Faculty of Electrical Engineering, Mathematics and Computer Science, TU Delft, Netherlands（电气工程、数学与计算机科学学院，代尔夫特理工大学，荷兰）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究了在线凸优化中正则化跟随者框架的动态遗憾保证，通过乐观组合未来成本和精心线性化过去成本，实现动态遗憾界，提出历史修剪方法以平衡懒惰与敏捷更新。
AI中文摘要：
我们重新审视在线凸优化中正则化跟随者（FTRL）框架，关注动态遗憾保证。先前工作指出，该框架在动态环境中因产生“懒惰”迭代而受限。然而，基于FTRL能够产生“敏捷”迭代的见解，我们证明其可通过乐观组合未来成本和精心线性化过去成本来恢复已知的动态遗憾界，这可能导致修剪部分成本。FTRL对动态比较器的新分析提供了一种在懒惰和敏捷更新之间插值的原理方法，带来更精细的遗憾项控制、无循环依赖的乐观性和类似AdaFTRL的最小递归正则化应用。更广泛地说，我们表明阻碍（乐观）动态遗憾的并非FTRL的“懒惰”投影风格，而是算法状态（线性化历史）与迭代之间的解耦，允许状态任意增长。相反，修剪在必要时同步这两个方面。
英文摘要：
We revisit the Follow the Regularized Leader (FTRL) framework for Online Convex Optimization (OCO) over compact sets, focusing on achieving dynamic regret guarantees. Prior work has highlighted the framework's limitations in dynamic environments due to its tendency to produce "lazy" iterates. However, building on insights showing FTRL's ability to produce "agile" iterates, we show that it can indeed recover known dynamic regret bounds through optimistic composition of future costs and careful linearization of past costs, which can lead to pruning some of them. This new analysis of FTRL against dynamic comparators yields a principled way to interpolate between lazy and agile updates and offers several benefits, including refined control over regret terms, optimism without cyclic dependence, and the application of minimal recursive regularization akin to AdaFTRL. More broadly, we show that it is not the "lazy" projection style of FTRL that hinders (optimistic) dynamic regret, but the decoupling of the algorithm's state (linearized history) from its iterates, allowing the state to grow arbitrarily. Instead, pruning synchronizes these two when necessary.
