Learning Fair and Preferable Allocations through Neural Network

The fair allocation of indivisible resources is a fundamental problem. Existing research has developed variousallocation mechanisms to satisfy different fairness notions. For example, round robin (RR) was proposed tomeet the fairness criterion known as envy-freeness up to one good (EF1). Experts’ heuristics without mathematicalformulations are used in real world resource allocation problems to find preferable outcomes for users. Therefore,we aim to design mechanisms that strictly satisfy good properties with replicating expert knowledge. However, thisproblem is challenging because such heuristic allocation mechanisms are often difficult to formalize mathematically,complicating their integration into theoretical frameworks. Additionally, formal mechanisms struggle to find preferableoutcomes, and directly replicating these implicit allocation mechanisms can result in unfair allocations becausehuman decision-making can introduce biases. In this paper, we aim to learn implicit allocation mechanisms fromexamples while strictly satisfying fairness constraints, specifically focusing on learning EF1 allocation mechanismsthrough supervised learning on examples of reported valuations and corresponding allocation outcomes produced byimplicit mechanisms. To address this, we developed a neural RR (NRR), a novel neural network that parameterizesRR. NRR is built from a differentiable relaxation of RR and can be trained to learn the agent ordering used forRR. We conducted experiments to learn EF1 allocation mechanisms from examples, demonstrating that our methodoutperforms baselines in terms of the proximity to the example allocations and qualities of predicted allocations.