Group-level Fairness Maximization in Online Bipartite Matching

Abstract

In typical online matching problems, the goal is to maximize the number of matches. This paper studies online bipartite matching from the perspective of group-level fairness, and the goal is to balance the number of matches made across different groups of online nodes. We assume that an online node's group belongings are revealed upon arrival, and measure performance based on the group with the smallest fraction of its nodes matched at the end. We distinguish between two different objectives: long-run fairness, where the algorithm is audited for its fairness over many realizations from the same instance; and short-run fairness, where the algorithm is audited for its fairness on a single realization.We focus on the known-IID model of online arrivals and analyze, under both objectives, the competitive ratio for two classes of algorithms: non-rejecting algorithms, which must match an online node as long as a neighbor is available; and general online algorithms, which are allowed to reject online nodes to improve fairness. For long-run fairness, we analyze two online algorithms (sampling and pooling) which establish asymptotic optimality across many different regimes (no specialized supplies, no rare demand types, or imbalanced supply/demand). By contrast, outside all of these regimes, we show that the competitive ratio for online algorithms is between 0.632 and 0.732. For short-run fairness, we focus on the case of a complete bipartite graph and show that the competitive ratio for online algorithms is between 0.863 and 0.942; we also derive a probabilistic rejection algorithm which is asymptotically optimal as total demand increases.

Fairness Maximization among Offline Agents in Online-Matching Markets

“…Unlike focusing on one single objective of fairness maximization like here, both studies in [36] and [37] seek to balance the objective of fairness maximization with that of profit maximization. Recently, Ma et al [38] considered a similar problem to us but focus on the fairness among online agents. Manshadi et al [39] studied fair online rationing such that each arriving agent can receive a fair share of resources proportional to its demand.…”

Fairer LP-based Online Allocation via Analytic Center

“…The authors prove that an approximation for such objective gives an allocation rule that achieves approximate Pareto-efficiency and envy-freeness. Ma and Xu (2020) formulate the online resource allocation problem into the online bipartite matching model.…”

Equity Promotion in Online Resource Allocation

“…Justification of parameters {𝜇 𝑔 }. Observe that previous studies (Ma, Xu, and Xu 2020;Nanda et al 2020;Xu and Xu 2020) have chosen a fairness metric as min 𝑔 ∈ G E[𝑋 𝑔 ]/E[ 𝐴 𝑔 ], the minimum ratio of the expected number of agents served to that of arrivals among all groups. This can be cast as a special case of ASR by setting each…”

“…One technical challenge in addressing (internal) equity promotion in online resource allocation is how to craft a proper metric of equity. Current metrics of equity proposed so far are all based on the minimum ratio of the number of requesters served to that of total arrivals within any given group (Ma, Xu, and Xu 2020;Nanda et al 2020;Xu and Xu 2020). Unfortunately, these metrics fail to capture the exact equity we expect in practice.…”