Fairer LP-based Online Allocation via Analytic Center

Abstract

In this paper, we consider a Linear Program (LP)-based online resource allocation problem where a decision maker accepts or rejects incoming customer requests irrevocably in order to maximize expected revenue given limited resources. At each time, a new order/customer/bid is revealed with a request of some resource(s) and a reward. We consider a stochastic setting where all the orders are i.i.d. sampled from an unknown distribution. Such formulation gives rise to many classic applications such as the canonical (quantity-based) network revenue management problem and the Adwords problem. Instead of focusing only on regret minimization, this paper aims to provide fairness guarantees while maintaining low regret. Our definition of fairness is that a fair online algorithm should treat similar agents/customers similarly and the decision made for similar individuals should be consistent over time. We define the fair offline solution as the analytic center of the offline optimal solution set, and define cumulative unfairness as the cumulative deviation from the online solutions to the fair offline solution. We propose a fair algorithm that uses an interior-point LP solver and dynamically detects unfair resource spending. Our algorithm can control cumulative unfairness on the scale of order O(log(T )), while maintaining the regret to be bounded without dependency on T . Moreover, we partially remove the nondegeneracy assumptions used in early results in the literature. This paper only requires the nondegeneracy condition for the binding constraints, and allows the existence of multiple optimal solutions.

Fairness-aware Network Revenue Management with Demand Learning

“…There is a vast body of literature considering the fairness in online allocation problem with inventory constraints (with known demand models) (Elzayn et al 2019, Ma et al 2020, Balseiro et al 2020, Chen et al 2021a, where the decision-maker must take an action upon each arriving our work is most related to (Balseiro et al 2020), we have thoroughly discussed the technical differences in the introduction section above and we will present the comparison more concretely in Section 3. We also note that (Balseiro et al 2020) works for the fairness-aware NRM problem in a quantity-based setting, where the decision-maker must irrevocably accept or reject each arriving request given limited resources (a special case of the online allocation problem studied in their paper).…”