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Differentially Private Machine Learning-powered Combinatorial Auction Design

Arash Jamshidi, Seyed Mohammad Hosseini, Seyed Mahdi Noormousavi, Mahdi Jafari Siavoshani

TL;DR

The paper tackles incentivizing truthful reporting in machine learning–powered combinatorial auctions by injecting differential privacy into the auction design. It leverages the Exponential Mechanism and DP stability to achieve (approximately) truthful behavior and analyzes both asymptotic and non-asymptotic regimes, providing SW guarantees such as $\mathrm{SW}(A_k^*) \ge \max_{A_k} \mathrm{SW}(A_k) - O\left(\frac{mk(\log n)^2}{n}\right)$ under suitable parameters. It introduces a Refined MLCA with a DP-based allocation step that attains $2\epsilon$-truthfulness and combines it with a punitive second-price auction to achieve exact truthfulness under specific assumptions. The results suggest that privacy-preserving adjustments can maintain high social welfare while ensuring bidders reveal truthful valuations, with implications for scalable, truthful design in privacy-conscious auction systems.

Abstract

We present a new approach to machine learning-powered combinatorial auctions, which is based on the principles of Differential Privacy. Our methodology guarantees that the auction mechanism is truthful, meaning that rational bidders have the incentive to reveal their true valuation functions. We achieve this by inducing truthfulness in the auction dynamics, ensuring that bidders consistently provide accurate information about their valuation functions. Our method not only ensures truthfulness but also preserves the efficiency of the original auction. This means that if the initial auction outputs an allocation with high social welfare, our modified truthful version of the auction will also achieve high social welfare. We use techniques from Differential Privacy, such as the Exponential Mechanism, to achieve these results. Additionally, we examine the application of differential privacy in auctions across both asymptotic and non-asymptotic regimes.

Differentially Private Machine Learning-powered Combinatorial Auction Design

TL;DR

The paper tackles incentivizing truthful reporting in machine learning–powered combinatorial auctions by injecting differential privacy into the auction design. It leverages the Exponential Mechanism and DP stability to achieve (approximately) truthful behavior and analyzes both asymptotic and non-asymptotic regimes, providing SW guarantees such as under suitable parameters. It introduces a Refined MLCA with a DP-based allocation step that attains -truthfulness and combines it with a punitive second-price auction to achieve exact truthfulness under specific assumptions. The results suggest that privacy-preserving adjustments can maintain high social welfare while ensuring bidders reveal truthful valuations, with implications for scalable, truthful design in privacy-conscious auction systems.

Abstract

We present a new approach to machine learning-powered combinatorial auctions, which is based on the principles of Differential Privacy. Our methodology guarantees that the auction mechanism is truthful, meaning that rational bidders have the incentive to reveal their true valuation functions. We achieve this by inducing truthfulness in the auction dynamics, ensuring that bidders consistently provide accurate information about their valuation functions. Our method not only ensures truthfulness but also preserves the efficiency of the original auction. This means that if the initial auction outputs an allocation with high social welfare, our modified truthful version of the auction will also achieve high social welfare. We use techniques from Differential Privacy, such as the Exponential Mechanism, to achieve these results. Additionally, we examine the application of differential privacy in auctions across both asymptotic and non-asymptotic regimes.
Paper Structure (12 sections, 7 theorems, 9 equations, 2 algorithms)

This paper contains 12 sections, 7 theorems, 9 equations, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Preliminaries
  4. Combinatorial Auctions
  5. Formal Model
  6. Vickrey-Clarke-Groves (VCG) Mechanism
  7. Differential Privacy
  8. Machine Learning-powered Combinatorial Auctions
  9. Differentially Private Auction Design
  10. Truthful Algorithm
  11. Discussion
  12. Conclusions

Key Result

Theorem 1

If the range of utilities for all players are in $[0,1]$ and If the mechanism $\mathcal{M}$ is $\epsilon$-differentially private then $\mathcal{M}$ is also $2\epsilon$-truthful.

Theorems & Definitions (14)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Definition 7
  • ...and 4 more