Online EFX Allocations with Predictions

Themistoklis Melissourgos, Nicos Protopapas

Keywords: online fair division, envy-freeness, algorithms with predictions, EFX

TL;DR: Approximate EFX is impossible in online fair division, even with identical valuations. We design a prediction-aware algorithm for two identical agents, whose fairness guarantees improve as prediction accuracy increases.

Abstract:

We study an online fair division problem where a fixed, but unknown number of goods arrive sequentially and must be allocated immediately and irrevocably to a given set of agents. The objective is to ensure (approximate) envy-freeness up to any good (EFX), that is, after the allocation, no agent should prefer another agent's bundle once any single good is removed from it. Unfortunately, we show that approximate EFX is impossible to guarantee in general, even under quite restrictive valuation assumptions. Specifically, our negative results hold even under identical valuations, in sharp contrast to the offline setting, where exact EFX allocations always exist.

To overcome this barrier, we follow the emerging trend of algorithms with predictions, assuming access to a vector of predicted valuations (e.g., produced by a machine-learning model). Predictions may be inaccurate, and we measure their error using the total variation distance from the true valuations. For additive valuations, we prove impossibility results for algorithms that either ignore predictions or rely solely on them, and we establish lower bounds on the prediction accuracy required by any algorithm to compute approximate EFX. Finally, we provide a positive result: for two agents with identical valuations, we design an algorithm that combines predictions with true values to approximate EFX, with guarantees that improve smoothly as prediction accuracy increases.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1272