Differentiable Combinatorial Auction Design: Optimizing Revenue-Welfare-Fairness Frontiers With Graph Attention Networks

Abstract

Designing optimal auctions for allocating public infrastructure-such as airport slots and energy resources-is challenging due to interdependent resources and complex side-constraints. While the Vickrey-Clarke-Groves (VCG) auction guarantees maximum welfare, it cannot maximize revenue or accommodate the multi-objective trade-offs inherent in public infrastructure systems. We propose a differentiable, constraint-aware framework for combinatorial auction design that enables end-to-end learning of fractionally feasible, approximately strategy-proof mechanisms. Our primary contribution is a combinatorial constraint enforcement technique that ensures fractional feasibility by construction, bypassing the need for penalty-based approximations. We introduce CAGraph, a novel graph-based architecture designed to capture dependencies between items and bidders, alongside CANet and CAFormer as deep learning baselines, for combinatorial settings. We also provide a Matching Pursuit-inspired decomposition that maps fractional allocations to feasible discrete allocations and empirically evaluates the resulting discretization gap. In synthetic benchmarks and an airport slot-divestiture case study, respectively, the learned mechanisms achieve up to 73.5% and 180% higher expected revenue than VCG, under small empirical regret. Finally, we visualize the Pareto frontiers for revenue, welfare, and fairness, providing regulators with a decision-support tool to design infrastructure auctions that balance profitability, efficiency and equity.