Fairer LP-based Online Allocation via Analytic Center
This work addresses fairness concerns in online allocation problems like network revenue management and Adwords, offering a novel approach that is incremental in method but provides specific gains in fairness and regret bounds.
The paper tackles the problem of ensuring fairness in online resource allocation by defining fairness as consistent treatment of similar customers over time and introducing cumulative unfairness as a metric. The proposed algorithm achieves O(log(T)) cumulative unfairness while maintaining bounded regret without dependency on T, under less restrictive assumptions on LP degeneracy.
In this paper, we consider an online resource allocation problem where a decision maker accepts or rejects incoming customer requests irrevocably in order to maximize expected reward 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 arises from many classic applications such as the canonical (quantity-based) network revenue management problem and the Adwords problem. While the literature on the topic mainly focuses on regret minimization, our paper considers the \textit{fairness} aspect of the problem. On a high level, we define the fairness in a way that a fair online algorithm should treat similar agents/customers similarly, and the decision made for similar agents/customers should be consistent over time. To achieve this goal, we define the fair offline solution as the analytic center of the offline optimal solution set, and introduce \textit{cumulative unfairness} as the cumulative deviation from the online solutions to the fair offline solution over time. We propose a fair algorithm based on an interior-point LP solver and a mechanism that dynamically detects unfair resource spending. Our algorithm achieves cumulative unfairness on the scale of order $O(\log(T))$, while maintains the regret to be bounded without dependency on $T$. In addition, compared to the literature, our result is produced under less restrictive assumptions on the degeneracy of the underlying linear program.