FAIRFORMER: A transformer architecture for discrete fair division

TL;DR

FAIRFORMER introduces a transformer-based neural network for fair division of indivisible goods, balancing efficiency and envy-freeness, and achieves near-optimal welfare with fast inference.

Contribution

It presents a novel permutation-equivariant transformer architecture for fair division that learns to allocate goods without supervision or explicit fairness labels.

Findings

Achieves 96-97% Nash welfare on sampled instances.

Outperforms baselines in solution quality and runtime.

Generalizes beyond training regime.

Abstract

We propose a deep neural network-based solution to the problem of allocating indivisible goods under additive subjective valuations without monetary transfers, trading off economic efficiency with envy-based fairness. We introduce FairFormer, an amortized, permutation-equivariant two-tower transformer that encodes items and agents as unordered token sets, applies self-attention within each set, and uses item-to-agent cross-attention to produce per-item assignment distributions in a single forward pass. FairFormer is trained end-to-end to maximize expected log-Nash welfare on sampled instances, requiring no solver supervision, unrolled allocation procedures, or fairness labels. At test time, we discretize by row-wise $\arg\max$ and apply a lightweight post-processing routine that transfers items to eliminate violations of envy-freeness up to one item while prioritizing improvements in Nash welfare. Our approach generalizes beyond its training regime and achieves near-optimal welfare (e.g., for uniformly sampled valuations, $96$--$97\%$ for Nash welfare; $95$--$96\%$ for utilitarian welfare), outperforming strong baselines in solution quality and/or runtime.