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Online Fair Division with Additional Information

Tzeh Yuan Neoh, Jannik Peters, Nicholas Teh

Abstract

We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and maximin share fairness (and their approximate variants), we investigate how access to future information changes what guarantees are achievable. Without any information, we prove strong impossibility results even for approximate fairness. With normalization information (agents' total values), we provide an algorithm that achieves stronger fairness guarantees than previously known results, and show matching impossibilities for stronger notions. With frequency predictions (value multisets without order), we design a meta-algorithm that lifts a broad class of offline ''share-based'' guarantees to the online setting, matching the best-known offline bounds. Finally, we provide learning-augmented variants of both models: under noisy totals or noisy frequency predictions, our guarantees are robust and degrade gracefully with the error parameters.

Online Fair Division with Additional Information

Abstract

We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and maximin share fairness (and their approximate variants), we investigate how access to future information changes what guarantees are achievable. Without any information, we prove strong impossibility results even for approximate fairness. With normalization information (agents' total values), we provide an algorithm that achieves stronger fairness guarantees than previously known results, and show matching impossibilities for stronger notions. With frequency predictions (value multisets without order), we design a meta-algorithm that lifts a broad class of offline ''share-based'' guarantees to the online setting, matching the best-known offline bounds. Finally, we provide learning-augmented variants of both models: under noisy totals or noisy frequency predictions, our guarantees are robust and degrade gracefully with the error parameters.

Paper Structure

This paper contains 19 sections, 20 theorems, 116 equations, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Further Related Work
  4. Online Fair Division.
  5. Learning-Augmented Online Fair Division
  6. Partial Information and Bandit Feedback.
  7. Online Social Choice
  8. Preliminaries
  9. Online Setting
  10. Impossibilities Without Information
  11. Normalization Information
  12. Learning-Augmented Guarantees under Noisy Normalization Information
  13. Frequency Predictions
  14. Learning-Augmented Guarantees under Noisy Frequency Predictions
  15. A simple instantiation rule.
  16. ...and 4 more sections

Key Result

Proposition 3.0

For $n \ge 2$, without future information, there does not exist any deterministic online algorithm with a competitive ratio strictly larger than $0$ with respect to EF1.

Theorems & Definitions (43)

  • Definition 2.1: EFX
  • Definition 2.2: EF1
  • Definition 2.3: PROP1
  • Definition 2.4: MMS
  • Proposition 3.0
  • proof
  • Example 3.1: KahanaHa2023
  • Theorem 3.2: benade2018envyvanish
  • Corollary 3.3
  • proof
  • ...and 33 more