Learning-Augmented Online Bipartite Fractional Matching

2025-05-25

AI Summary

This paper studies online fractional bipartite matching with learning-augmented advice, addressing both vertex-weighted and unweighted variants. Under the setting where high-quality matching suggestions are available upon each arriving vertex, we propose a novel randomized hybrid strategy—first rigorously surpassing the classical “coin-flip” benchmark in theory. We extend the approach to the AdWords problem under the small-bid assumption, achieving a significantly improved competitive ratio, and establish a tight lower bound for the robustness–consistency trade-off. Theoretical analysis shows that our algorithm attains near-optimal competitive ratios across multiple settings. Extensive experiments on synthetic and real-world datasets validate its practical performance gains. This work introduces a new paradigm for learning-augmented online matching and provides rigorous theoretical foundations for integrating predictions into online algorithms.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

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.

Problem

• Improving online bipartite fractional matching with learning-augmented advice
• Dominating naive strategies in vertex-weighted and unweighted matching variants
• Extending algorithms to AdWords problem under small bids assumption

Innovation

• Learning-augmented online bipartite fractional matching
• Vertex-weighted and unweighted algorithm variants
• AdWords problem extension with small bids