Dynamic Learning in Large Matching Markets

Anand Kalvit, assaf zeevi

Keywords: multi-armed bandits, matching, learning, regret, algorithms, explore-then-commit, infinitely many arms

TL;DR: We propose a rate-optimal algorithm for the dynamic matching problem over n rounds with jobs arriving in batches of stochastic size and composition, and an unlimited supply of workers governed by a latent distribution.

Abstract: We study a sequential matching problem faced by "large" centralized platforms where "jobs" must be matched to "workers" subject to uncertainty about worker skill proficiencies. Jobs arrive at discrete times with "job-types" observable upon arrival. To capture the "choice overload" phenomenon, we posit an unlimited supply of workers where each worker is characterized by a vector of attributes (aka "worker-types") drawn from an underlying population-level distribution. The distribution as well as mean payoffs for possible worker-job type-pairs are unobservables and the platform's goal is to sequentially match incoming jobs to workers in a way that maximizes its cumulative payoffs over the planning horizon. We establish lower bounds on the "regret" of any matching algorithm in this setting and propose a novel rate-optimal learning algorithm that adapts to aforementioned primitives "online." Our learning guarantees highlight a distinctive characteristic of the problem: achievable performance only has a "second-order" dependence on worker-type distributions; we believe this finding may be of interest more broadly.