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Statistically Truthful Auctions via Acceptance Rule

Roy Maor Lotan, Inbal Talgam-Cohen, Yaniv Romano

TL;DR

The paper tackles the lack of strategy-proofness guarantees in data-driven auctions by introducing a probabilistic notion of truthfulness. It develops Statistically Truthful Auctions via Acceptance Rule (SPACE), combining a neural regret predictor with conformal-calibration based acceptance to guarantee the maximal regret $\ell_{\text{rgt}}$ with probability $1-\alpha$. The approach supports both shared-backbone and black-box regret-estimation architectures and provides a formal theorem under iid assumptions, showing that accepted test auctions meet the target regret while maintaining revenue close to a strong baseline. This delivers a practical, scalable path to reliable, revenue-efficient data-driven auctions with test-time guarantees for truthful bidding.

Abstract

Auctions are key for maximizing sellers' revenue and ensuring truthful bidding among buyers. Recently, an approach known as differentiable economics based on machine learning (ML) has shown promise in learning powerful auction mechanisms for multiple items and participants. However, this approach has no guarantee of strategy-proofness at test time. Strategy-proofness is crucial as it ensures that buyers are incentivized to bid their true valuations, leading to optimal and fair auction outcomes without the risk of manipulation. In this work, we propose a formulation of statistical strategy-proofness for auction mechanisms. Specifically, we offer a method that bounds the regret -- quantifying deviation from truthful bidding -- below a pre-specified level with high probability. Building upon conformal prediction techniques, we develop an auction acceptance rule that leverages regret predictions to guarantee that the data-driven auction mechanism meets the statistical strategy-proofness requirement with high probability. Our method -- Statistically Truthful Auctions via Acceptance Rule (STAR) -- represents a practical middle-ground between two extremes: enforcing truthfulness -- zero-regret -- at the cost of significant revenue loss, and naively using ML to construct auctions with the hope of attaining low regret, with no test-time guarantees.

Statistically Truthful Auctions via Acceptance Rule

TL;DR

The paper tackles the lack of strategy-proofness guarantees in data-driven auctions by introducing a probabilistic notion of truthfulness. It develops Statistically Truthful Auctions via Acceptance Rule (SPACE), combining a neural regret predictor with conformal-calibration based acceptance to guarantee the maximal regret with probability . The approach supports both shared-backbone and black-box regret-estimation architectures and provides a formal theorem under iid assumptions, showing that accepted test auctions meet the target regret while maintaining revenue close to a strong baseline. This delivers a practical, scalable path to reliable, revenue-efficient data-driven auctions with test-time guarantees for truthful bidding.

Abstract

Auctions are key for maximizing sellers' revenue and ensuring truthful bidding among buyers. Recently, an approach known as differentiable economics based on machine learning (ML) has shown promise in learning powerful auction mechanisms for multiple items and participants. However, this approach has no guarantee of strategy-proofness at test time. Strategy-proofness is crucial as it ensures that buyers are incentivized to bid their true valuations, leading to optimal and fair auction outcomes without the risk of manipulation. In this work, we propose a formulation of statistical strategy-proofness for auction mechanisms. Specifically, we offer a method that bounds the regret -- quantifying deviation from truthful bidding -- below a pre-specified level with high probability. Building upon conformal prediction techniques, we develop an auction acceptance rule that leverages regret predictions to guarantee that the data-driven auction mechanism meets the statistical strategy-proofness requirement with high probability. Our method -- Statistically Truthful Auctions via Acceptance Rule (STAR) -- represents a practical middle-ground between two extremes: enforcing truthfulness -- zero-regret -- at the cost of significant revenue loss, and naively using ML to construct auctions with the hope of attaining low regret, with no test-time guarantees.
Paper Structure (17 sections, 2 theorems, 10 equations, 8 figures, 6 tables, 1 algorithm)

This paper contains 17 sections, 2 theorems, 10 equations, 8 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Challenge of Strategy-Proofness in Data-Driven Auctions
  3. Related Work
  4. Overview of Contributions
  5. Background
  6. Problem Setup
  7. Conformal Prediction
  8. Proposed Method
  9. Regret Estimation
  10. Model Calibration
  11. Experiments
  12. Discussion
  13. Additional Experiments
  14. Mathematical Proofs
  15. Experiment setup and environment
  16. ...and 2 more sections

Key Result

Theorem 2.1

Assume that the calibration set ${\mathcal{D}_\textup{cal} = \{x_i, y_i\}}_{k = 1}^{K}$ and the test point $(x_\textup{test}, y_\textup{test})$ are i.i.d. samples from $P_{x,y}$. Then, the following coverage guarantee holds for $\mathcal{C}(x_\textup{test})$ defined in eq:conformal_set:

Figures (8)

  • Figure 1: Overview of Statistically Proofed Auctions via Conformal Estimation (SPACE ). Bidders submit bids for multiple items, forming a bid matrix. An auction model (mechanism) processes these bids to determine allocation and payment. A regret model estimates the incentive to deviate from truthful bidding. Using regret predictions and holdout calibration data, a selective acceptance rule ensures statistical strategy-proofness, accepting only outcomes with low estimated regret. This balances revenue and incentive compatibility.
  • Figure 2: Regret behavior of RegretNet in the $2$-bidder, $3$-item auction setting. For additional details on the experimental configuration of this model, please refer to Section \ref{['sec:exp_setup']}.
  • Figure 3: Comparison of revenue across different auction mechanisms. Strategy-proof methods (green) ensure truthful bidding, but yield lower revenue. Non-strategy-proof methods (red) achieve higher revenue at the cost of truthfulness. Our proposed statistically strategy-proof mechanism (blue) balances revenue and strategy-proofness. See Table \ref{['tab:results_rev']} for references.
  • Figure 4: Distribution of regret values for RegretNet and SPACE in the $2\times3$ auction setting. The test and calibration sets each contain 1,000 examples. The red dashed line indicates the requested regret level $\mathop{\mathrm{\ell_{\mathop{\mathrm{\textbf{rgt}}}\nolimits}}}\nolimits$.
  • Figure 5: Boxplot of the true regret values for SPACE in the $2\times3$ auction setting. The test and calibration sets each contain 1,000 examples. The red dashed line indicates the requested regret level $\mathop{\mathrm{\ell_{\mathop{\mathrm{\textbf{rgt}}}\nolimits}}}\nolimits$.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Theorem 2.1: Conformal Coverage Guarantee; Vovk, Gammerman, and Saunders vovk1999machine
  • Definition 3.1: Statistically Strategy-Proof Auctions
  • Proposition 1
  • proof