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We study an online allocation problem with sequentially arriving items andadversarially chosen agent values, with the goal of balancing fairness andefficiency. Our goal is to study the performance of algorithms that achievestrong guarantees under other input models such as stochastic inputs, in orderto achieve robust guarantees against a variety of inputs. To that end, we studythe PACE (Pacing According to Current Estimated utility) algorithm, an existingalgorithm designed for stochastic input. We show that in the equal-budgetscase, PACE is equivalent to the integral greedy algorithm. We go on to showthat with natural restrictions on the adversarial input model, both integralgreedy allocation and PACE have asymptotically bounded multiplicative envy aswell as competitive ratio for Nash welfare, with the multiplicative factorseither constant or with optimal order dependence on the number of agents. Thiscompletes a "best-of-many-worlds" guarantee for PACE, since past work showedthat PACE achieves guarantees for stationary and stochastic-but-non-stationaryinput models.

Greedy-Based Online Fair Allocation with Adversarial Input: Enabling Best-of-Many-Worlds Guarantees