Fair Resource Allocation Algorithm for an Online Environment

Abstract

This work addresses learning online fair division, wherein the values of items that arrive sequentially are not directly observable, but instead the noisy, estimated values are observable when we assign the items. We consider the problem as computing market equilibria in linear Fisher markets where agents have additive utilities. In such markets, the static allocation simultaneously achieves envy-freeness and Pareto optimality by maximizing Nash social welfare, assuming that items are divisible or can be allocated randomly. However, this fact is no longer valid in online settings. To this end, we have developed online algorithms that combine dual averaging with multi-armed bandit indices. Through dual averaging, our algorithms gradually learn the values of arriving items via bandit feedback. As a result, the algorithms asymptotically achieve the optimal Nash social welfare. We also empirically demonstrate the superior performance of the proposed algorithms in synthetic and empirical datasets.