Online Budgeted Matching with General Bids
Jianyi Yang, Pengfei Li, Adam Wierman, Shaolei Ren

TL;DR
This paper addresses the online budgeted matching problem with general bids, removing the fractional last matching assumption, establishing upper bounds, and proposing a versatile meta algorithm with provable competitive ratios.
Contribution
It introduces MetaAd, a novel meta algorithm that handles general bids without the FLM assumption and extends to learning-augmented settings.
Findings
Upper bound of 1-k on competitive ratio for any deterministic algorithm
MetaAd reduces to different algorithms with provable ratios based on k
Extended MetaAd to FLM setting with competitive guarantees
Abstract
Online Budgeted Matching (OBM) is a classic problem with important applications in online advertising, online service matching, revenue management, and beyond. Traditional online algorithms typically assume a small bid setting, where the maximum bid-to-budget ratio (\kappa) is infinitesimally small. While recent algorithms have tried to address scenarios with non-small or general bids, they often rely on the Fractional Last Matching (FLM) assumption, which allows for accepting partial bids when the remaining budget is insufficient. This assumption, however, does not hold for many applications with indivisible bids. In this paper, we remove the FLM assumption and tackle the open problem of OBM with general bids. We first establish an upper bound of 1-\kappa on the competitive ratio for any deterministic online algorithm. We then propose a novel meta algorithm, called MetaAd, which…
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Taxonomy
TopicsAuction Theory and Applications · Game Theory and Voting Systems · Optimization and Search Problems
Methodstravel james
