Bridging the Gap Between Estimated and True Regret Towards Reliable Regret Estimation in Deep Learning based Mechanism Design

TL;DR

This paper identifies systematic underestimation of regret in deep learning auction models, introduces a lower bound and refined approximation method to improve regret estimation accuracy, and emphasizes the importance of reassessing prior claims.

Contribution

It presents a new lower bound and an item-wise regret approximation, along with a guided refinement procedure, to enhance the reliability of regret estimation in deep learning auctions.

Findings

Existing methods significantly underestimate true regret.

The proposed approach improves regret estimation accuracy.

Reevaluation of prior deep learning auction models is necessary.

Abstract

Recent advances, such as RegretNet, ALGnet, RegretFormer and CITransNet, use deep learning to approximate optimal multi item auctions by relaxing incentive compatibility (IC) and measuring its violation via ex post regret. However, the true accuracy of these regret estimates remains unclear. Computing exact regret is computationally intractable, and current models rely on gradient based optimizers whose outcomes depend heavily on hyperparameter choices. Through extensive experiments, we reveal that existing methods systematically underestimate actual regret (In some models, the true regret is several hundred times larger than the reported regret), leading to overstated claims of IC and revenue. To address this issue, we derive a lower bound on regret and introduce an efficient item wise regret approximation. Building on this, we propose a guided refinement procedure that substantially improves regret estimation accuracy while reducing computational cost. Our method provides a more reliable foundation for evaluating incentive compatibility in deep learning based auction mechanisms and highlights the need to reassess prior performance claims in this area.