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

Shuyuan You, Zhiqiang Zhuang, Kewen Wang, Zhe Wang

TL;DR

The paper tackles the reliability gap in regret estimation for deep learning–based mechanism design by deriving a mathematically grounded lower bound on ex-post regret and introducing an efficient item-wise regret proxy. It then presents a hybrid Item-wise Guided Gradient Refinement that combines discrete item-wise insights with continuous optimisation to yield accurate regret estimates at much lower computational cost. Empirical results across RegretNet, ALGnet, RegretFormer, and CITransNet reveal pervasive underestimation of IC violations in high-dimensional settings, with RegretFormer showing particularly catastrophic underestimation. The proposed framework enables robust IC assessment and suggests that many reported revenues in prior work may be achieved under non-IC conditions, underscoring the need to reassess existing claims.

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.

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

TL;DR

The paper tackles the reliability gap in regret estimation for deep learning–based mechanism design by deriving a mathematically grounded lower bound on ex-post regret and introducing an efficient item-wise regret proxy. It then presents a hybrid Item-wise Guided Gradient Refinement that combines discrete item-wise insights with continuous optimisation to yield accurate regret estimates at much lower computational cost. Empirical results across RegretNet, ALGnet, RegretFormer, and CITransNet reveal pervasive underestimation of IC violations in high-dimensional settings, with RegretFormer showing particularly catastrophic underestimation. The proposed framework enables robust IC assessment and suggests that many reported revenues in prior work may be achieved under non-IC conditions, underscoring the need to reassess existing claims.

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.
Paper Structure (19 sections, 8 theorems, 17 equations, 7 tables)

This paper contains 19 sections, 8 theorems, 17 equations, 7 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Empirical Analysis of Regret Underestimation in Deep-learning Based Mechanisms
  4. Hyperparameter Heterogeneity and Cross-Validation
  5. Hyperparameter Sensitivity and Convergence Analysis
  6. Method
  7. Mathematical Lower Bound of Regret
  8. Item-wise Regret
  9. Item-wise Guided Gradient Refinement
  10. Experiments
  11. Hyperparameter Selection and Rationale
  12. Validating Our Approach on ALGnet
  13. Re-evaluating State-of-the-Art Models
  14. Conclusion
  15. Proof of Proposition 1
  16. ...and 4 more sections

Key Result

Proposition 1

The time complexity for calculating the optimal regret for all bidders is $O(n \cdot Q^m)$, where $n$ is the number of bidders and $m$ is the number of items.

Theorems & Definitions (12)

  • Proposition 1
  • Theorem 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • proof
  • Theorem 2
  • proof
  • Proposition 5
  • proof
  • ...and 2 more