Regret, stability & fairness in matching markets with bandit learners

Abstract

We consider the two-sided matching market with bandit learners. In the standard matching problem, users and providers are matched to ensure incentive compatibility via the notion of stability. However, contrary to the core assumption of the matching problem, users and providers do not know their true preferences a priori and must learn them. To address this assumption, recent works propose to blend the matching and multi-armed bandit problems. They establish that it is possible to assign matchings that are stable (i.e., incentive-compatible) at every time step while also allowing agents to learn enough so that the system converges to matchings that are stable under the agents' true preferences. However, while some agents may incur low regret under these matchings, others can incur high regret-specifically, Ω(T ) optimal regret, where T is the time horizon. In this work, we incorporate costs and transfers in the two-sided matching market with bandit learners in order to faithfully model competition between agents. We prove that, under our framework, it is possible to simultaneously guarantee four desiderata:(1) incentive compatibility, i.e., stability, (2) low regret, i.e., O(log(T )) optimal regret, (3) fairness in the distribution of regret among agents, and (4) high social welfare.1 Initialize matching M : A → A such that M (a) ← ∅ for all a ∈ A; 2 Initialize empty (FIFO) queues Q(p) ← [] for all p ∈ P;// Fill each provider's queue with users in order of decreasing preference. 3 for p ∈ P do 4 for i = 1, 2, . . . , N do 5 Append r −1 (i; V (p, •)) to Q(p); // Add p's i-th ranked user. 6 end 7 end // As long as there exists a provider who is unmatched... 8 while ∃p ∈ P : M (p) = ∅ do 9 u ← pop(Q(p)); // Provider p's favorite user of those remaining in p's queue. // If user u is unmatched, match u and p. 10 if M (u) = ∅ then 11 M (u) ← p; 12 M (p) ← u; // If user u prefers p to its current match M (u), match u and p.13 else if V (u, p) > V (u, M (u)) then 14 M ′ (M (u)) ← ∅; 15 M (u) ← p; 16 M (p) ← u; 17 end 18 Return M ;

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.…”

Pessimism meets VCG: Learning Dynamic Mechanism Design via Offline Reinforcement Learning

“…Kandasamy et al (2020) provided an algorithm that recovers the VCG mechanism in a stationary multi-arm bandit setting. Cen and Shah (2021), Dai and Jordan (2021), Jagadeesan et al (2021), and Liu et al (2021) studied the recovery of stable matching when the agents' utilities are given by bandit feedback. Balcan et al (2008) shows that incentive-compatible mechanism design problems can be reduced to a structural risk minimization problem.…”

Rate-Optimal Contextual Online Matching Bandit

“…For example, monetary transfer is prohibited in the job application market. In a similar setting, Cen and Shah (2021) considers the case when both users and providers do not know their true preferences a priori. They incorporate costs and money transfers among agents to faithfully model the competition among agents and discuss the fairness in the matching.…”