在双方偏好未知的匹配问题中,高效找到最优稳定匹配。
Probably Correct Optimal Stable Matching under Two-Sided Uncertainty

- 基于部分偏好信息设计消除算法,动态筛选最优匹配
- 理论证明可在有限轮次内以高概率识别最优稳定匹配
- 适合需可靠匹配的场景,如人才分配、资源调度
我们研究双面市场中稳定匹配的序列学习问题,双方初始偏好均未知。在中心化设定下,算法每步匹配个体并接收反映其偏好的噪声奖励,遵循半盲反馈结构。采用纯探索视角,目标是高效以高概率识别最优稳定匹配。工作扩展了先前结果,处理双面不确定性并利用部分偏好信息。核心思想是引入广义稳定匹配概念,使在部分偏好下仍可识别最优匹配。提出基于消除的算法,其停止条件利用已学部分偏好的结构,并提供精细化样本复杂度分析。除纯探索外,还将方法扩展至后悔最小化,建立相对于最优稳定匹配的后悔上界,避免依赖最小奖励差距Δ_min。
原文摘要 · Abstract (English)
We study a sequential learning problem for stable matchings in two-sided markets where preferences on both sides are initially unknown. We focus on a centralized setting where an algorithm matches agents at each time step and receives noisy rewards that reflect the preferences of the matched agents, following a semi-bandit feedback structure. We adopt a pure exploration perspective, aiming to efficiently identify the optimal stable matching with high probability. Our work extends prior results by handling \emph{two-sided uncertainty} and by exploiting \emph{partial preference} information. A central ingredient is the notion of \textbf{pervasive stable matching}, which enables the identification of optimal stable matchings under partial preferences. We propose elimination-based algorithms whose stopping criteria exploit the structure of the learned partial preferences, and provide a refined sample-complexity analysis. Beyond pure exploration, we extend our approach to regret minimization and establish regret bounds with respect to the \emph{optimal} stable matching that avoid dependence on the minimum reward gap $Δ_{\min}$.
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