在线学习与博弈中的最优交替遗憾
Optimal Alternating Regret for Online Learning and Games
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中文总结 AI 辅助
该研究解决在线线性与凸优化的交替遗憾问题，提出OLO和OCO的最优算法，改进了此前的遗憾界，获得更快的博弈均衡收敛速度，还证明了对应的下界。
中文摘要 AI 辅助
我们针对在线线性优化（OLO）和在线凸优化（OCO），解决了由博弈中交替学习动态所驱动的遗憾概念——极小极大最优交替遗憾。对于在概率单纯形Δ_d上的OLO，我们提出了一种算法，其交替遗憾为O(log d)，且对于任意时间跨度T，该遗憾保持为常数，并给出了匹配的下界。我们的常数遗憾界显著改进了之前的结果：遗憾为O(log^(2/3)d · T^(1/3))[Cevher、Cutkosky、Kavis、Piliouras、Skoulakis、Viano，NeurIPS 2023；Hait、Li、Luo、Zhang，COLT 2025]。因此，我们获得的交替学习动态在两人零和博弈中收敛到纳什均衡的速度为O(log d / T)，在两人一般和博弈中收敛到粗相关均衡（CCE）的速度为O(log d / T)。这是首个在两人一般和博弈中实现O(1/T)收敛到CCE的非耦合学习动态，而所有先前工作都带有额外的log T因子。对于在d维紧凸集上的一般OCO，我们提出了一种算法，其交替遗憾为O(d log(1+T/d))，改进了之前的最优结果\tilde{O}(d^(2/3)T^(1/3))。我们还证明了匹配的下界为Ω(d log(1+T/d))，表明Ω(log T)因子是不可避免的。
英文摘要
We settle the minimax-optimal alternating regret, a regret notion motivated by alternating learning dynamics in games, for both online linear optimization (OLO) and online convex optimization (OCO). For OLO over the probability simplex $Δ_d$, we give an algorithm with $O(\log d)$ alternating regret that remains a constant for any time horizon $T$, and a matching lower bound. Our constant regret bound significantly improves previous results with $O(\log ^{2/3}d \cdot T^{1/3})$ regret [Cevher, Cutkosky, Kavis, Piliouras, Skoulakis, Viano, NeurIPS 2023, Hait, Li, Luo, Zhang, COLT 2025]. As a result, we obtain alternating learning dynamics with $O(\log d /T)$ convergence to Nash equilibria in two-player zero-sum games and $O(\log d /T)$ convergence to coarse correlated equilibria in two-player general-sum games. This is the first uncoupled learning dynamics with $O(1/T)$ convergence to CCE in two-player general-sum games, while all prior works suffer additional $\log T$ factors. For general OCO over a $d$-dimensional compact convex set, we give an algorithm with $O(d\log (1+T/d))$ alternating regret, improving the previous best of $\widetilde{O}(d^{2/3}T^{1/3})$. We also prove a matching lower bound of $Ω(d\log (1+T/d))$, showing that the $Ω(\log T)$ factor is unavoidable.
发表机构
- Shanghai University of Finance and Economics（上海财经大学）
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
