#### Sequential Fair Allocation of Limited Resources under Stochastic Demands

##### Sean R. Sinclair, Gauri Jain, Siddhartha Banerjee, Christina Lee Yu

We consider the problem of dividing limited resources between a set of agents arriving sequentially with unknown (stochastic) utilities. Our goal is to find a fair allocation - one that is simultaneously Pareto-efficient and envy-free. When all utilities are known upfront, the above desiderata are simultaneously achievable (and efficiently computable) for a large class of utility functions. In a sequential setting, however, no policy can guarantee these desiderata simultaneously for all possible utility realizations. A natural online fair allocation objective is to minimize the deviation of each agent's final allocation from their fair allocation in hindsight. This translates into simultaneous guarantees for both Pareto-efficiency and envy-freeness. However, the resulting dynamic program has state-space which is exponential in the number of agents. We propose a simple policy, HopeOnline, that instead aims to match' the ex-post fair allocation vector using the current available resources and predicted' histogram of future utilities. We demonstrate the effectiveness of our policy compared to other heurstics on a dataset inspired by mobile food-bank allocations.

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