Exploring the Tradeoff between Competitive Ratio and Variance in Online-Matching Markets

TL;DR

This paper introduces two policies for online matching markets that balance the competitive ratio and variance, improving performance and providing asymptotic optimality under large budgets.

Contribution

It proposes two linear-programming-based policies to optimize the tradeoff between competitive ratio and variance in online matching, with one achieving asymptotic optimality.

Findings

SAMP policy achieves asymptotically optimal competitive ratio.

ATT policy improves over existing methods in competitive ratio.

The model captures correlated cost and utility in diverse online markets.

Abstract

In this paper, we propose an online-matching-based model to study the assignment problems arising in a wide range of online-matching markets, including online recommendations, ride-hailing platforms, and crowdsourcing markets. It features that each assignment can request a random set of resources and yield a random utility, and the two (cost and utility) can be arbitrarily correlated with each other. We present two linear-programming-based parameterized policies to study the tradeoff between the \emph{competitive ratio} (CR) on the total utilities and the \emph{variance} on the total number of matches (unweighted version). The first one (SAMP) is to sample an edge according to the distribution extracted from the clairvoyant optimal, while the second (ATT) features a time-adaptive attenuation framework that leads to an improvement over the state-of-the-art competitive-ratio result. We also consider the problem under a large-budget assumption and show that SAMP achieves asymptotically optimal performance in terms of competitive ratio.