Beyond $\log^2(T)$ Regret for Decentralized Bandits in Matching Markets

Abstract

We design decentralized algorithms for regret minimization in two sided matching markets with one-sided bandit feedback that significantly improves upon the prior works [23,27,24]. First, for general markets, for any ε>0, we design an algorithm that achieves a O(log 1+ε (T )) regret to the agent-optimal stable matching, with unknown time horizon T , improving upon the O(log 2 (T )) regret achieved in [24]. Second, we provide the optimal Θ(log(T )) regret for markets satisfying uniqueness consistency -markets where leaving participants don't alter the original stable matching. Previously, Θ(log(T )) regret was achievable [27,24] in the much restricted serial dictatorship setting, when all arms have the same preference over the agents. We propose a phase based algorithm, where in each phase, besides deleting the globally communicated dominated arms, the agents locally delete arms with which they collide often. This local deletion is pivotal in breaking deadlocks arising from rank heterogeneity of agents across arms. We further demonstrate superiority of our algorithm over existing works through simulations.

Learn to Match with No Regret: Reinforcement Learning in Markov Matching Markets

“…There is an emerging line of research on learning stable matchings with bandit feedback (Das and Kamenica, 2005;Liu et al, 2020Liu et al, , 2021Sankararaman et al, 2021;Cen and Shah, 2021;Basu et al, 2021) using the mature tools from the bandit literature. Most of them focus on matchings with non-transferable utilities (Gale and Shapley, 1962), which fails to capture real-world markets with monetary transfers between agents, e.g., payments from passengers to drivers on ride-hailing platforms.…”

“…The data streams that arise from digital markets provide opportunities to cope with such challenges, via learning-based mechanism design. Recent work (Jagadeesan et al, 2021;Liu et al, 2021;Sankararaman et al, 2021;Basu et al, 2021) has begun to apply modern machine learning tools to problems in adaptive mechanism design. One particular area of focus in learning-aware market design has been matching, a class of problems central to microeconomics (Mas-Colell et al, 1995).…”

Decentralized Learning in Online Queuing Systems

“…While collisions can be used as communication tools between players in multiplayer bandits [Bistritz and Leshem, 2018, Boursier and Perchet, 2019, Mehrabian et al, 2020, Wang et al, 2020, this becomes harder with an asymmetric colli-sion model as in competing bandits. However, some level of communication remains possible [Sankararaman et al, 2020, Basu et al, 2021. In queuing systems, collisions are not only asymmetric, but depend on the age of the sent packets, making such solutions unsuited.…”

Decentralized, Communication- and Coordination-free Learning in Structured Matching Markets

“…If, at a given round, multiple agents request the same firm, the firm-assumed to be a myopic utility maximizer-accepts the request of its most preferred agent (who receives a noisy measurement of their utility of the match from which they can learn their preferences) and rejects the others (who receive no information about their preferences). This setup serves has been studied in a line of recent works on online matching markets [LMJ20,LRMJ21,SBS21,BSS21].…”

“…Successful algorithms for this framework must simultaneously solve a statistical learning problem (that of learning about their own preferences) and a competitive problem (ensuring that agents get their most desired match despite the presence of other self-interested agents in the market). Previous works for addressing this problem propose algorithms that are centralized [LMJ20] (whereby agents send their current beliefs over their preferences to a central platform which does the matching), require coordination between agents (i.e., a choreographed set of strategies to minimize rejections) [SBS21,BSS21], or require agents to fully observe the market outcomes of other agents [LRMJ21]. In contrast, the DA algorithm-which we take to be the full-information benchmark to which we compare algorithms-is (i) fully decentralized, (ii) coordination-free, and (iii) requires agents to make decisions only based upon their own history of rejections and successful matchings.…”