Learning for Edge-Weighted Online Bipartite Matching with Robustness Guarantees
This work addresses the trade-off between average and worst-case performance in online matching problems, which is incremental but important for applications like online advertising.
The paper tackles the problem of online bipartite matching, such as in ad display, by proposing LOMAR, a reinforcement learning-based approach that combines expert algorithms with RL decisions via an online switching operation to achieve both good average-case performance and worst-case robustness guarantees, with experiments showing advantages over existing baselines.
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 $ρ\in[0,1]$, LOMAR is $ρ$-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