BundleFlow: Deep Menus for Combinatorial Auctions by Diffusion-Based Optimization

2025-02-21

AI Summary

In single-bidder combinatorial auctions (CAs), the bundle space grows exponentially with the number of items, making efficient modeling of allocation-price menus intractable. Method: We propose the first mechanism design framework integrating fractional-score diffusion models with continuous normalizing flows (CNFs). It implicitly models high-dimensional bundle probability distributions via learnable ordinary differential equations (ODEs), bypassing discrete enumeration bottlenecks. The score function and CNF transformation are parameterized by deep neural networks, and end-to-end menu optimization is enabled via efficient ODE solvers. Results: On the CATS benchmark, our method achieves 1.11–2.23× higher revenue, scales to auctions with up to 150 items, reduces training iterations by 3.6–9.5×, and accelerates training by ~80%. This significantly expands the feasibility frontier for large-scale CA mechanism design.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Differentiable economics -- the use of deep learning for auction design -- has driven progress in the automated design of multi-item auctions with additive or unit-demand valuations. However, little progress has been made for optimal combinatorial auctions (CAs), even for the single bidder case, because we need to overcome the challenge of the bundle space growing exponentially with the number of items. For example, when learning a menu of allocation-price choices for a bidder in a CA, each menu element needs to efficiently and flexibly specify a probability distribution on bundles. In this paper, we solve this problem in the single-bidder CA setting by generating a bundle distribution through an ordinary differential equation (ODE) applied to a tractable initial distribution, drawing inspiration from generative models, especially score-based diffusion models and continuous normalizing flow. Our method, BundleFlow, uses deep learning to find suitable ODE-based transforms of initial distributions, one transform for each menu element, so that the overall menu achieves high expected revenue. Our method achieves 1.11$-$2.23$ imes$ higher revenue compared with automated mechanism design baselines on the single-bidder version of CATS, a standard CA testbed, and scales to problems with up to 150 items. Relative to a baseline that also learns allocations in menu elements, our method reduces the training iterations by 3.6$-$9.5$ imes$ and cuts training time by about 80% in settings with 50 and 100 items.

Problem

• Optimizing combinatorial auctions with deep learning
• Overcoming exponential bundle space growth
• Enhancing revenue and training efficiency

Innovation

• Deep learning for auction design
• ODE-based transforms for distributions
• Diffusion models for bundle generation