We study the problem of online unweighted bipartite matching with $n$ offline
vertices and $n$ online vertices where one wishes to be competitive against the
optimal offline algorithm. While the classic RANKING algorithm of Karp et al.
[1990] provably attains competitive ratio of $1-1/e > 1/2$, we show that no
learning-augmented method can be both 1-consistent and strictly better than
$1/2$-robust under the adversarial arrival model. Meanwhile, under the random
arrival model, we show how one can utilize methods from distribution testing to
design an algorithm that takes in external advice about the online vertices and
provably achieves competitive ratio interpolating between any ratio attainable
by advice-free methods and the optimal ratio of 1, depending on the advice
quality.

研究在线非加权二分图匹配中的问题，其中有 n 个离线顶点和 n 个在线顶点，并且希望与最佳离线算法保持竞争力。尽管 Karp 等人 [1990] 的经典 RANKING 算法可以证明达到 1-1/e>1/2 的竞争比率，但我们表明在对抗性到达模型中，没有学习增强方法既可以是 1 - 一致的又可以比 1/2 - 健壮。同时，在随机到达模型下，我们展示了如何利用分布测试方法设计出一种算法，该算法接受关于在线顶点的外部建议，并在竞争比率上从不需要建议的方法和最优比率 1 之间插值，这取决于建议的质量。