Online EFX Allocations with Predictions

2025-08-06

AI Summary

This paper studies online fair allocation: a fixed number of indivisible items arrive sequentially and must be irrevocably assigned to multiple agents in real time, aiming to achieve envy-freeness up to any removed good (EFX) ex post. Since exact EFX is unattainable in the online setting, we introduce— for the first time—prediction-augmented mechanisms. Leveraging an additive valuation model and total variation distance to quantify prediction error, we design a dynamic allocation algorithm that jointly incorporates predictions and real-time feedback. We prove that neither ignoring predictions nor relying on them exclusively guarantees approximate EFX. For two agents with identical valuations, we propose the first provably approximate EFX algorithm, whose approximation ratio monotonically improves with prediction accuracy. This work pioneers the integration of predictive information into online fair division, establishing a new paradigm for prediction-enhanced online fairness.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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 valuations, that is, the percentage of predicted value-mass that disagrees with the true values. Focusing on the natural class of additive valuations, we prove impossibility results even on approximate EFX allocations for algorithms that either ignore predictions or rely solely on them. We then turn to algorithms that use both the predictions and the true values and show strong lower bounds on the prediction accuracy that is required by any algorithm to compute an approximate EFX. These negative results persist even under identical valuations, contrary to the offline setting where exact EFX allocations always exist without the necessity of predictions. We then present an algorithm for two agents with identical valuations that uses effectively the predictions and the true values. The algorithm approximates EFX, with its guarantees improving as the accuracy of the predictions increases.

Problem

• Online fair division of sequential goods with EFX goal
• Impossibility of approximate EFX without reliable predictions
• Algorithm for two agents using predictions to approximate EFX

Innovation

• Online EFX allocations using prediction vectors
• Algorithms combining predictions and true values
• EFX approximation improves with prediction accuracy