Finding an optimal matching in a weighted graph is a standard combinatorial problem. We consider its semi-bandit version where either a pair or a full matching is sampled sequentially. We prove that it is possible to leverage a rank-1 assumption on the adjacency matrix to reduce the sample complexity and the regret of off-the-shelf algorithms up to reaching a linear dependency in the number of vertices (up to poly log terms).

翻译：在加权图表中找到最佳匹配是一个标准组合问题。 我们考虑的是其半斜体版本, 即对对或完全匹配按顺序取样。 我们证明, 可以利用对相邻矩阵的一级假设来降低抽样复杂性和现成算法的遗憾, 直至达到顶点数的线性依赖性( 直至 IP 日志 术语 ) 。