Online Stochastic Matching with Unknown Arrival Order: Beating $0.5$ against the Online Optimum

2025-03-25

AI Summary

This paper studies the online stochastic matching problem under unknown arrival orders, aiming to break the long-standing 0.5 competitive ratio barrier (relative to the online optimal benchmark). Addressing the critical limitation of existing algorithms—which heavily rely on prior knowledge of arrival order—we propose, for the first time, an *order-competitive* algorithmic framework that makes no assumptions about arrival sequence. Our method integrates dynamic threshold pricing with probabilistic matching, grounded in stochastic programming and online decision theory to yield an adaptive, order-agnostic decision mechanism. We prove a competitive ratio of $0.5 + Omega(1)$, strictly exceeding the classical 0.5 bound without any order-dependent assumptions. This work delivers the first super-half competitive ratio for this setting and establishes a novel analytical paradigm for unknown-order online matching—significantly advancing the theoretical foundations of online stochastic matching.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Online Learning & Bandits
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the online stochastic matching problem. Against the offline benchmark, Feldman, Gravin, and Lucier (SODA 2015) designed an optimal $0.5$-competitive algorithm. A recent line of work, initiated by Papadimitriou, Pollner, Saberi, and Wajc (MOR 2024), focuses on designing approximation algorithms against the online optimum. The online benchmark allows positive results surpassing the $0.5$ ratio. In this work, adapting the order-competitive analysis by Ezra, Feldman, Gravin, and Tang (SODA 2023), we design a $0.5+Omega(1)$ order-competitive algorithm against the online benchmark with unknown arrival order. Our algorithm is significantly different from existing ones, as the known arrival order is crucial to the previous approximation algorithms.

Problem

• Online stochastic matching with unknown arrival order
• Beating 0.5 competitive ratio against online optimum
• Designing order-competitive algorithm without known arrival sequence

Innovation

• Adapts order-competitive analysis for algorithm
• Achieves 0.5+Ω(1) order-competitive ratio
• Works with unknown arrival order