Learning-Augmented Online Bipartite Fractional Matching

TL;DR

This paper introduces learning-augmented algorithms for online bipartite fractional matching, improving performance by leveraging advice, extending to AdWords, and validating with experiments.

Contribution

It develops new algorithms that outperform naive strategies in online bipartite fractional matching using advice, and extends to AdWords with improved guarantees.

Findings

Algorithms outperform naive strategies in experiments.

Extension to AdWords yields significant improvements.

Hardness bounds on robustness and consistency tradeoff.

Abstract

Online bipartite matching is a fundamental problem in online optimization, extensively studied both in its integral and fractional forms due to its theoretical significance and practical applications, such as online advertising and resource allocation. Motivated by recent progress in learning-augmented algorithms, we study online bipartite fractional matching when the algorithm is given advice in the form of a suggested matching in each iteration. We develop algorithms for both the vertex-weighted and unweighted variants that provably dominate the naive "coin flip" strategy of randomly choosing between the advice-following and advice-free algorithms. Moreover, our algorithm for the vertex-weighted setting extends to the AdWords problem under the small bids assumption, yielding a significant improvement over the seminal work of Mahdian, Nazerzadeh, and Saberi (EC 2007, TALG 2012). Complementing our positive results, we establish a hardness bound on the robustness-consistency tradeoff that is attainable by any algorithm. We empirically validate our algorithms through experiments on synthetic and real-world data.