EEF1-NN: Efficient and EF1 allocations through Neural Networks

TL;DR

This paper introduces EEF1-NN, a neural network model that efficiently finds allocations that are approximately envy-free up to one item and maximize social welfare, outperforming existing methods in speed and quality.

Contribution

The paper presents a novel neural network architecture, inspired by UNet, for efficiently approximating EF1 and maximum social welfare allocations in fair division problems.

Findings

EEF1-NN achieves near-optimal social welfare in allocations.

The model guarantees high probability of EF1 across various distributions.

EEF1-NN is faster and more scalable than traditional optimization methods.

Abstract

Neural networks have shown state-of-the-art performance in designing auctions, where the network learns the optimal allocations and payment rule to ensure desirable properties. Motivated by the same, we focus on learning fair division of resources, with no payments involved. Our goal is to allocate the items, goods and/or chores efficiently among the fair allocations. By fair, we mean an allocation that is Envy-free (EF). However, such an allocation may not always exist for indivisible resources. Therefore, we consider the relaxed notion, Envy-freeness up to one item (EF1) that is guaranteed to exist. However, it is not enough to guarantee EF1 since the allocation of empty bundles is also EF1. Hence, we add the further constraint of efficiency, maximum utilitarian social welfare (USW). In general finding, USW allocations among EF1 is an NP-Hard problem even when valuations are additive. In this work, we design a network for this task which we refer to as EEF1-NN. We propose an UNet inspired architecture, Lagrangian loss function, and training procedure to obtain desired results. We show that EEF1-NN finds allocation close to optimal USW allocation and ensures EF1 with a high probability for different distributions over input valuations. Compared to existing approaches EEF1-NN empirically guarantees higher USW. Moreover, EEF1-NN is scalable and determines the allocations much faster than solving it as a constrained optimization problem.