Online EFX Allocations with Predictions
Themistoklis Melissourgos, Nicos Protopapas

TL;DR
This paper investigates online fair division with predictions, proving limitations of algorithms relying solely on predictions or true values, and proposing an algorithm that improves EFX approximation as prediction accuracy increases.
Contribution
It introduces the first analysis of online EFX allocations with predictions, establishing lower bounds and presenting an algorithm that leverages prediction accuracy for better fairness guarantees.
Findings
Approximate EFX allocations are impossible without predictions.
Algorithms relying only on predictions or true values face strong lower bounds.
An algorithm for two agents with identical valuations improves as prediction accuracy increases.
Abstract
We study an online fair division problem where a fixed number of goods arrive sequentially and must be allocated to a given set of agents. Once a good arrives, its true value for each agent is revealed, and it has to be immediately and irrevocably allocated to some agent. The ultimate goal is to ensure envy-freeness up to any good (EFX) after all goods have been allocated. Unfortunately, as we show, approximate EFX allocations are unattainable in general, even under restrictive assumptions on the valuation functions. To address this, we follow a recent and fruitful trend of augmenting algorithms with predictions. Specifically, we assume access to a prediction vector estimating the agents' true valuations -- e.g., generated by a machine learning model trained on past data. Predictions may be unreliable, and we measure their error using the total variation distance from the true…
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