Online Fair Allocation with Best-of-Many-Worlds Guarantees

TL;DR

The paper tackles online fair allocation with sequential item arrivals and additive agent utilities, seeking allocations that balance fairness (envy- and proportionality-like notions) with efficiency (Nash welfare). It introduces unconstrained PACE, a tuning-free online dynamic that can be viewed as both an unregularized dual-averaging method on the Eisenberg-Gale dual and a primal integral greedy rule, achieving best-of-many-worlds guarantees across stationary, nonstationary, and adversarial inputs. Theoretical results establish convergence rates under i.i.d. inputs, robustness to nonstationarity, and worst-case guarantees for adversarial inputs, while empirical results on real datasets corroborate strong performance under realistic temporal arrivals. The work advances online market-equilibrium thinking by removing projection constraints, yielding simple, decentralized algorithms with strong theoretical and practical implications for large-scale online fair division tasks.

Abstract

We investigate the online fair allocation problem with sequentially arriving items under various input models, with the goal of balancing fairness and efficiency. We propose the unconstrained PACE (Pacing According to Current Estimated utility) algorithm, a parameter-free allocation dynamic that requires no prior knowledge of the input while using only integral allocations. PACE attains near-optimal convergence or approximation guarantees under stationary, stochastic-but-nonstationary, and adversarial input types, thereby achieving the first best-of-many-worlds guarantee in online fair allocation. Beyond theoretical bounds, PACE is highly simple, efficient, and decentralized, and is thus likely to perform well on a broad range of real-world inputs. Numerical results support the conclusion that PACE works well under a variety of input models. We find that PACE performs very well on two real-world datasets even under the true temporal arrivals in the data, which are highly nonstationary.