Advancing Differentiable Economics: A Neural Network Framework for Revenue-Maximizing Combinatorial Auction Mechanisms

TL;DR

This paper tackles revenue-maximizing combinatorial auctions with private bundle-valuations by extending differentiable economics into the CA domain. It introduces two neural architectures, CANet and CAFormer, to learn randomized mechanisms while enforcing combinatorial feasibility via a differentiable allocation decomposition and gradient-based augmented Lagrangian training. Empirically, both architectures surpass heuristic baselines and RegretNet variants in combinatorial settings, with CAFormer achieving the best revenue and negligible regret, and CANet offering competitive performance with permutation-sensitive variants. The work provides a scalable, flexible framework for differentiable mechanism design in combinatorial domains and points to future extensions to online and unknown-distribution environments.

Abstract

Differentiable economics, which uses neural networks as function approximators and gradient-based optimization in automated mechanism design (AMD), marked a significant breakthrough with the introduction of RegretNet \citep{regretnet_paper}. It combines the flexibility of deep learning with a regret-based approach to relax incentive compatibility, allowing for approximations of revenue-maximizing auctions. However, applying these techniques to combinatorial auctions (CAs) - where bidders value bundles rather than individual items, capturing item interdependencies - remains a challenge, primarily due to the lack of methodologies that can effectively deal with combinatorial constraints. To tackle this, we propose two architectures: CANet, a fully connected neural network, and CAFormer, a transformer-based model designed to learn optimal randomized mechanisms. Unlike existing methods in traditional AMD, our approach is more scalable and free of assumptions about the structures of allowable bundles or bidder valuations. We demonstrate that our models match current methods in non-combinatorial settings and set new benchmarks for CAs. Specifically, our models consistently outperform benchmark mechanisms derived from heuristic approaches and provide empirical solutions where analytical results are unavailable. This work bridges the gap in applying differentiable economics to combinatorial auctions, offering a scalable and flexible framework for designing revenue-maximizing mechanisms.

Figures (1)

• Figure 1: CANet and CAFormer Architectures.

Theorems & Definitions (3)

• Theorem 1: Birkhoff, 1916
• Lemma 1
• proof