Duality for Optimal Multi-Item, Multi-Bidder Auction Design: Revenue Certificates through Deep Learning

2026-06-08

AI Summary

This work addresses the absence of closed-form revenue-optimal solutions in multi-item, multi-bidder auctions with continuous type spaces by proposing the first deep learning framework tailored to the dual formulation of this setting. The approach parameterizes Lagrange multipliers satisfying flow conservation constraints via neural networks and employs gradient-based optimization to compute feasible dual solutions. Furthermore, it introduces a novel lifting technique applicable to arbitrary continuous distributions, which maps coarse-grained discrete solutions into the continuous domain to yield provable revenue upper bounds. The method successfully recovers known analytical solutions and generates tight upper bounds in complex environments, thereby verifying the near-optimality of existing dominant-strategy incentive-compatible (DSIC) mechanisms.

Abstract

Characterizing revenue-optimal auctions for multi-item, multi-bidder settings remains a fundamental open problem, with no known closed-form solution existing beyond restrictive binary-type instances. This has motivated interest in computational approaches to optimal auction design. In this paper, we introduce the first computational framework that directly tackles the dual problem for multi-item, multi-bidder auctions and dominant-strategy incentive compatibility (DSIC), generating certified revenue upper bounds. Our approach parametrizes Lagrange multipliers with a structurally guaranteed strict flow-conservation property using neural networks, enabling efficient optimization over feasible dual solutions via gradient descent. To bridge the gap between discrete computational methods and theoretical guarantees for continuous types, we develop a novel lifting technique that maps dual certificates from coarse discretizations to fine refinements. We prove that lifting gives valid revenue upper bounds for multi-item, multi-bidder auctions with continuous uniform valuations. Furthermore, we give a generalized lifting construction for arbitrary continuous distributions and demonstrate that these lifted duals converge to the revenue of the original continuous problem in the discrete limit. We validate this computational framework for the dual auction design problem by recovering known analytical mechanisms for canonical instances. For multi-item multi-bidder problems, our framework establishes a small gap between the optimal revenue and best-known DSIC mechanisms, providing computational certificates of near-optimality.

Problem

• optimal auction design
• multi-item multi-bidder
• revenue maximization
• dominant-strategy incentive compatibility
• duality

Innovation

• dual auction design
• revenue certification
• neural network parametrization
• lifting technique
• dominant-strategy incentive compatibility