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In this paper, we consider an online resource allocation problem where adecision maker accepts or rejects incoming customer requests irrevocably inorder to maximize expected reward given limited resources. At each time, a neworder/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 froman unknown distribution. Such formulation arises from many classic applicationssuch as the canonical (quantity-based) network revenue management problem andthe Adwords problem. While the literature on the topic mainly focuses on regretminimization, 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 algorithmshould treat similar agents/customers similarly, and the decision made forsimilar agents/customers should be consistent over time. To achieve this goal,we define the fair offline solution as the analytic center of the offlineoptimal solution set, and introduce \textit{cumulative unfairness} as thecumulative deviation from the online solutions to the fair offline solutionover time. We propose a fair algorithm based on an interior-point LP solver anda mechanism that dynamically detects unfair resource spending. Our algorithmachieves cumulative unfairness on the scale of order $O(\log(T))$, whilemaintains the regret to be bounded without dependency on $T$. In addition,compared to the literature, our result is produced under less restrictiveassumptions on the degeneracy of the underlying linear program.

Fairer LP-based Online Allocation via Analytic Center