Online Bipartite Matching with Advice: Tight Robustness-Consistency Tradeoffs for the Two-Stage Model

Abstract

We study the two-stage vertex-weighted online bipartite matching problem of Feng, Niazadeh, and Saberi (SODA '21) in a setting where the algorithm has access to a suggested matching that is recommended in the first stage. We evaluate an algorithm by its robustness R, which is its performance relative to that of the optimal offline matching, and its consistency C, which is its performance when the advice or the prediction given is correct. We characterize for this problem the Pareto-efficient frontier between robustness and consistency, which is rare in the literature on advice-augmented algorithms, yet necessary for quantifying such an algorithm to be optimal. Specifically, we propose an algorithm that is R-robust and C-consistent for any (R, C) with 0 ≤ R ≤ 3 4 and, and prove that no other algorithm can achieve a better tradeoff.

Online Resource Allocation with Samples

“…Our class of algorithms contributes to a recent literature on using ML advice in the online algorithm design. Examples include Lykouris and Vassilvtiskii (2018) and Rohatgi (2020) for online caching problems, Antoniadis et al (2020) for online secretary problems, Jin and Ma (2022) for online matching problems, Lattanzi et al (2020) for online scheduling with job weight advice, and Balseiro et al (2022) for an online resource allocation problem. 1…”

Scheduling with Speed Predictions

“…The goal is to design algorithms that achieve stronger bounds when the provided predictions are accurate, which are called consistency bounds, but also maintain worst-case robustness bounds that hold even when the predictions are inaccurate. Optimization problems that have been studied under this framework include online paging [20], scheduling [24], secretary [10], covering [6], matching [8,9,17], knapsack [16], facility location [13], Nash social welfare [7], and graph [4] problems. Most of the work on scheduling in this model has considered predictions about the processing times of the jobs [24,21,18,5,15,2,3].…”