Advancing Differentiable Mechanism Design: Neural Architectures for Combinatorial Auctions

Mai Pham, Vikrant Vaze, Peter Chin

Keywords: combinatorial auctions, mechanism design, constraint-aware neural network

Abstract: Designing optimal auctions has major real-world impact, but remains notoriously difficult to solve analytically, often intractable in strategic or high-dimensional settings. Neural networks have recently approximated optimal mechanisms in multi-item auctions, yet extending them to combinatorial auctions (CAs) is harder. The main challenge is enforcing combinatorial feasibility, as bundle allocations involve non-convex, binary, and overlapping constraints beyond standard neural architectures. This paper introduces a novel combinatorial constraint enforcement technique for deep learning, applied to a fully connected network (CANet) and a transformer-based network (CAFormer). We also present CAGraph, a graph attention network (GAT) model that formulates the winner determination problem as set packing and captures interdependencies between bidders and bundles. Our approach yields three key results. First, our models consistently outperform heuristic baselines and prior learning-based methods—including RegretNet—across diverse synthetic combinatorial auction settings. Second, in real-world airport slot auctions, they maintain low regret while flexibly balancing welfare and revenue. Third, in a cyber defense case study, a defensive agent uses the auction's output to allocate limited resources to vulnerable network hosts, demonstrating the practical versatility of our framework. Together, these results demonstrate the flexibility, scalability, and effectiveness of differentiable, constraint-aware neural architectures for combinatorial mechanism design.

Submission Number: 42