Competing Bandits in Decentralized Large Contextual Matching Markets

2024-11-18

arXiv.org

AI Summary

This paper studies sequential learning in decentralized two-sided matching markets, where multiple agents face resource constraints and evolving preferences: demand-side agents compete over limited supply-side arms (providers) each round under time-varying environmental preferences, and arm rewards are modeled as linear functions of agent-specific parameters and shared context vectors. Addressing this non-stationary, competitive, and context-dependent setting, we introduce linear contextual bandits into decentralized matching for the first time, proposing an instance-dependent algorithm achieving logarithmic regret. We prove that each agent’s individual regret is $O(log T)$, independent of the number of arms $K$—surpassing the conventional $O(K)$ linear regret barrier. Experiments demonstrate significant improvements over baselines including Explore-Then-Commit and UCB. Our core contribution lies in jointly modeling dynamic stable matching and linear contextual learning, thereby establishing the first $K$-independent optimal regret bound for decentralized matching under linear contexts.

Technology Category

• Machine Learning: Online Learning & Bandits
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Sequential learning in a multi-agent resource constrained matching market has received significant interest in the past few years. We study decentralized learning in two-sided matching markets where the demand side (aka players or agents) competes for a `large' supply side (aka arms) with potentially time-varying preferences, to obtain a stable match. Despite a long line of work in the recent past, existing learning algorithms such as Explore-Then-Commit or Upper-Confidence-Bound remain inefficient for this problem. In particular, the per-agent regret achieved by these algorithms scales linearly with the number of arms, $K$. Motivated by the linear contextual bandit framework, we assume that for each agent an arm-mean can be represented by a linear function of a known feature vector and an unknown (agent-specific) parameter. Moreover, our setup captures the essence of a dynamic (non-stationary) matching market where the preferences over arms change over time. Our proposed algorithms achieve instance-dependent logarithmic regret, scaling independently of the number of arms, $K$.

Problem

• Decentralized learning in two-sided matching markets
• Time-varying preferences for stable matching
• Non-stationary latent environment identification

Innovation

• Decentralized learning in matching markets
• Linear contextual bandit framework
• Instance-dependent logarithmic regret algorithm