Learning for Edge-Weighted Online Bipartite Matching with Robustness Guarantees

TL;DR

This paper introduces LOMAR, a novel reinforcement learning approach for online bipartite matching that guarantees robustness and competitive performance, balancing worst-case guarantees with improved average-case results.

Contribution

The paper proposes a new online switching operation in RL-based matching, providing robustness guarantees and balancing average and worst-case performance.

Findings

LOMAR achieves $ ho$-competitiveness for any $ ho ext{ in }[0,1]$.

Empirical results show LOMAR outperforms existing baselines.

The approach effectively balances robustness and average performance.

Abstract

Many problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but it lacks robustness and can perform arbitrarily poorly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judicious condition to hedge against future uncertainties, decides whether to follow the expert's decision or the RL decision for each online item. We prove that for any $\rho\in[0,1]$, LOMAR is $\rho$-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines. Our code is available at: https://github.com/Ren-Research/LOMAR