[Paper Review] Decentralized, Communication- and Coordination-free Learning in Structured Matching Markets

Chinmay Maheshwari, Eric Mazumdar+1 more|arXiv (Cornell University)|Jun 6, 2022

Game Theory and Voting Systems4 citations

TL;DR

This paper proposes decentralized, communication- and coordination-free learning algorithms for agents in structured two-sided matching markets, where agents learn their preferences through repeated interactions without knowing others' strategies. The algorithms achieve logarithmic regret in time horizon under α-reducible preference structures, proving that competition does not severely degrade performance in stable matching settings.

ABSTRACT

We study the problem of online learning in competitive settings in the context of two-sided matching markets. In particular, one side of the market, the agents, must learn about their preferences over the other side, the firms, through repeated interaction while competing with other agents for successful matches. We propose a class of decentralized, communication- and coordination-free algorithms that agents can use to reach to their stable match in structured matching markets. In contrast to prior works, the proposed algorithms make decisions based solely on an agent's own history of play and requires no foreknowledge of the firms' preferences. Our algorithms are constructed by splitting up the statistical problem of learning one's preferences, from noisy observations, from the problem of competing for firms. We show that under realistic structural assumptions on the underlying preferences of the agents and firms, the proposed algorithms incur a regret which grows at most logarithmically in the time horizon. Our results show that, in the case of matching markets, competition need not drastically affect the performance of decentralized, communication and coordination free online learning algorithms.

Motivation & Objective

• Address the challenge of online learning in competitive two-sided matching markets where agents lack prior knowledge of their preferences.
• Design algorithms that operate without communication, coordination, or global market state observation, ensuring scalability and privacy.
• Achieve stable matching convergence with minimal regret despite competition from other self-interested agents.
• Establish theoretical guarantees for regret growth under realistic structural assumptions on agent and firm preferences.

Proposed method

• Decompose the learning problem into separate statistical learning (from noisy match utilities) and competitive matching (handling collisions with other agents).
• Use a two-phase algorithm: first, Thompson Sampling or UCB-based exploration to estimate personal preferences; second, a stable matching selection mechanism based on empirical utility estimates.
• Leverage α-reducible preference structures (e.g., serial dictatorship, no-crossing conditions) to ensure unique stable matching and tractable regret analysis.
• Model firm behavior as myopic utility maximizers that accept the highest-ranked agent among those who request them.
• Bound regret by analyzing collision and pulling frequencies using concentration inequalities and martingale arguments.
• Introduce indicators for successful matches, rejections, and pruning of suboptimal firms to track learning progress and regret components.

Experimental results

Research questions

• RQ1 Can decentralized, coordination-free algorithms achieve stable matching convergence in two-sided online matching markets with incomplete preference information?
• RQ2 What is the fundamental trade-off between exploration (learning preferences) and competition (avoiding rejections) in such settings?
• RQ3 How does competition affect the regret of decentralized learning algorithms in structured matching markets?
• RQ4 Can logarithmic regret be achieved without communication, coordination, or full observation of other agents’ actions?
• RQ5 Under what structural assumptions on preferences does a unique stable matching exist, and how does this enable efficient learning?

Key findings

• The proposed algorithms achieve a regret bound that grows at most logarithmically in the time horizon T, specifically O(log T) under α-reducible preference structures.
• Regret is bounded by O(1/Δ² log(1/Δ) + log T) for suboptimal firms, where Δ is the utility gap between the stable match and a suboptimal firm.
• The algorithm maintains decentralized operation: agents make decisions based solely on their own history of rejections and match outcomes.
• Coordination-free and communication-free design ensures scalability and privacy in large-scale online markets.
• The framework supports realistic market structures such as serial dictatorship and no-crossing conditions, which are common in real-world platforms.
• Empirical mean estimates of utility are updated based on noisy match feedback, and the algorithm effectively balances exploration and exploitation without global coordination.