发表机构
University of Bonn; Institute of Computer Science, University of Bonn; Microsoft Research; PUC-Rio; Georgia Tech; School of Mathematics, Georgia Tech; School of Computer Science, Georgia Tech（波恩大学; 波恩大学计算机科学学院; 微软研究院; 里约热内卢天主教大学; 佐治亚理工学院; 佐治亚理工学院数学学院; 佐治亚理工学院计算机科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究基于极小极大视角提出后验匹配原理，将在线算法竞争分析简化为贝叶斯在线设计，为多类在线问题提供最优或接近最优保证，构建了可复用的理论框架。
AI 中文摘要
竞争分析是在线算法研究的核心，但上界往往高度依赖具体问题。我们通过极小极大视角开发了一种更具普适性的方法。基于Yao原理，我们将最坏情况竞争分析简化为在到达序列的任意相关先验下的贝叶斯在线设计。对于此类先验，设X*为已实现实例的事后最优分数解，且X^(t)=E[X*|F_t]为其后验过程。我们的指导规则是后验匹配：在每个时刻t，选择满足在线约束且尽可能跟踪当前后验X^(t)的可行在线动作。我们证明，这一单一原理可为多个经典在线分数问题提供最优或接近最优的保证，包括集合覆盖、负载均衡、匹配及更一般的资源分配问题，在这些场景中恢复或改进了基于范数/凹目标的现有最优界。通过已知的取整归约，它还为加权分页、星型度量上的MTS（度量任务系统）及滑雪租赁问题提供了随机整数保证。从技术层面看，我们的分析将竞争保证简化为离线最优后验生成的向量鞅的关键概率不等式。所得框架为从任意相关先验下的贝叶斯在线设计到信息论最坏情况竞争保证提供了可复用的路径。
英文摘要
Competitive analysis is central to the study of online algorithms, but upper bounds are often highly problem-specific. We develop a more unifying methodology via the minimax viewpoint. Guided by Yao's principle, we reduce worst-case competitive analysis to Bayesian online design under an arbitrary correlated prior over arrival sequences. For such a prior, let $X^*$ be the hindsight-optimal fractional solution for the realized instance, and let $X^{(t)}=\mathbb E[X^*\mid \mathcal F_t]$ be its posterior process. Our guiding rule is posterior matching: at each time $t$, choose the feasible online action that tracks the current posterior $X^{(t)}$ as closely as the online constraints permit. We show that this single principle yields optimal or near-optimal guarantees for several classical online fractional problems, including set cover, load balancing, matching and more general resource-allocation problems, recovering or improving state-of-the-art bounds in these settings with norm/concave objectives. Via known rounding reductions, it also yields randomized integral guarantees for weighted paging, MTS on star metrics, and ski-rental. At a technical level, our analysis reduces competitive guarantees to key probabilistic inequalities for the vector martingales generated by the posterior of the offline optimum. The resulting framework gives a reusable route from Bayesian online design under arbitrary correlated priors to information-theoretic worst-case competitive guarantees.
CommentsTo appear at FOCS 2026
