Matching While Learning

Johari, Ramesh; Kamble, Vijay; Kanoria, Yash

doi:10.1287/opre.2020.2013

Cited by 33 publications

(15 citation statements)

References 28 publications

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“…Many of these papers consider a multi-armed bandit setting where rewards are stochastic and redrawn i.i.d. from an unknown distribution, with algorithms of an explore-exploit nature [13,26,31]. Efficient algorithms that approximate the optimal online algorithm were also studied by [41] in a stochastic setting with a price for querying each edge, relying on a Gittins Index characterization for the optimal online algorithm [15,42].…”

Section: Relationship With Prior Workmentioning

confidence: 99%

Decentralized Matching in a Probabilistic Environment

Jeloudar

Pollner

et al. 2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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We consider a model for repeated stochastic matching where compatibility is probabilistic, is realized the first time agents are matched, and persists in the future. Such a model has applications in the gig economy, kidney exchange, and mentorship matching.We ask whether a decentralized matching process can approximate the optimal online algorithm. In particular, we consider a decentralized stable matching process where agents match with the most compatible partner who does not prefer matching with someone else, and known compatible pairs continue matching in all future rounds. We demonstrate that the above process provides a 0.316-approximation to the optimal online algorithm for matching on general graphs. We also provide a 1 /7-approximation for many-to-one bipartite matching, a 1 /11-approximation for capacitated matching on general graphs, and a 1 /2 -approximation for forming teams of up to agents. Our results rely on a novel coupling argument that decomposes the successful edges of the optimal online algorithm in terms of their round-by-round comparison with stable matching.

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Section: Relationship With Prior Workmentioning

confidence: 99%

Decentralized Matching in a Probabilistic Environment

Jeloudar

Pollner

et al. 2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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“…As a generalization of a paired kidney exchange market, the dynamic matching problem was extended to finding disjoint 3-way circles and chains [19,3,6,9,34]. Anderson et al [5] and Ashlagi et al [8] analyzed the expected waiting time in the market.…”

Section: Stochastic Matching Marketmentioning

confidence: 99%

“…Matching Market with Departures A matching market where each agent is allowed to leave has been studied in various settings. Johari et al [19] and Ashlagi et al [7] studied a matching model where agents would depart after a constant time after arrival. Akbarpour et al [4] introduced a dynamic model where each vertex arrives and departs stochastically on a general (i.e., non-bipartite) network.…”

Section: Stochastic Matching Marketmentioning

confidence: 99%

Dynamic Bipartite Matching Market with Arrivals and Departures

Kakimura¹,

Zhu²

2021

Preprint

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In this paper, we study a matching market model on a bipartite network where agents on each side arrive and depart stochastically by a Poisson process. For such a dynamic model, we design a mechanism that decides not only which agents to match, but also when to match them, to minimize the expected number of unmatched agents. The main contribution of this paper is to achieve theoretical bounds on the performance of local mechanisms with different timing properties. We show that an algorithm that waits to thicken the market, called the Patient algorithm, is exponentially better than the Greedy algorithm, i.e., an algorithm that matches agents greedily. This means that waiting has substantial benefits on maximizing a matching over a bipartite network. We remark that the Patient algorithm requires the planner to identify agents who are about to leave the market, and, under the requirement, the Patient algorithm is shown to be an optimal algorithm. We also show that, without the requirement, the Greedy algorithm is almost optimal. In addition, we consider the 1-sided algorithms where only an agent on one side can attempt to match. This models a practical matching market such as a freight exchange market and a labor market where only agents on one side can make a decision. For this setting, we prove that the Greedy and Patient algorithms admit the same performance, that is, waiting to thicken the market is not valuable. This conclusion is in contrast to the case where agents on both sides can make a decision and the non-bipartite case by [Akbarpour et al., Journal of Political Economy, 2020].

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“…TaskRabbit, UpWork, DoorDash. An emerging line of research [1,16,23,27,24] in the field of multi-agent bandits is dedicated to understanding algorithmic principles in the interplay of competition, learning and regret minimization. The two-sided matching market [14] is one such thread, where regret minimization is first studied in [23] with a centralized arbiter, and in [27,24] at different levels of decentralization.…”

Section: Introductionmentioning

confidence: 99%

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

Basu,

Sankararaman,

Sankararaman

2021

Preprint

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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.

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Matching While Learning

Cited by 33 publications

References 28 publications

Decentralized Matching in a Probabilistic Environment

Decentralized Matching in a Probabilistic Environment

Dynamic Bipartite Matching Market with Arrivals and Departures

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

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