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Data Auctions for Retrieval Augmented Generation

Minbiao Han, Seyed A. Esmaeili, Michael Albert, Haifeng Xu

TL;DR

The paper addresses exclusive data auctions for Retrieval Augmented Generation by modeling bidder value with a coverage-based function and proving NP-hardness for welfare maximization even with two bidders. It introduces a practical $(1-1/e)$-approximation via LP relaxation and rounding (LPR) and then a monotone post-processing step called data burning (LPRMono) to achieve incentive compatibility without sacrificing the approximation. A generalized Myerson framework guides truthfulness, and experiments on synthetic and real image/text data demonstrate competitive revenue and truthful behavior compared to baselines. Overall, the work advances data market design for RAG by delivering IC, approximately optimal allocation algorithms suitable for exclusive data settings and scalable to real datasets.

Abstract

We study the problem of data selling for Retrieval Augmented Generation (RAG) tasks in Generative AI applications. We model each buyer's valuation of a dataset with a natural coverage-based valuation function that increases with the inclusion of more relevant data points that would enhance responses to anticipated queries. Motivated by issues such as data control and prior-free revenue maximization, we focus on the scenario where each data point can be allocated to only one buyer. We show that the problem of welfare maximization in this setting is NP-hard even with two bidders, but design a polynomial-time $(1-1/e)$ approximation algorithm for any number of bidders. Unfortunately, however, this efficient allocation algorithm fails to be incentive compatible. The crux of our approach is a carefully tailored post-processing step called data burning which retains the $(1-1/e)$ approximation factor but achieves incentive compatibility. Our thorough experiments on synthetic and real-world image and text datasets demonstrate the practical effectiveness of our algorithm compared to popular baseline algorithms for combinatorial auctions.

Data Auctions for Retrieval Augmented Generation

TL;DR

The paper addresses exclusive data auctions for Retrieval Augmented Generation by modeling bidder value with a coverage-based function and proving NP-hardness for welfare maximization even with two bidders. It introduces a practical -approximation via LP relaxation and rounding (LPR) and then a monotone post-processing step called data burning (LPRMono) to achieve incentive compatibility without sacrificing the approximation. A generalized Myerson framework guides truthfulness, and experiments on synthetic and real image/text data demonstrate competitive revenue and truthful behavior compared to baselines. Overall, the work advances data market design for RAG by delivering IC, approximately optimal allocation algorithms suitable for exclusive data settings and scalable to real datasets.

Abstract

We study the problem of data selling for Retrieval Augmented Generation (RAG) tasks in Generative AI applications. We model each buyer's valuation of a dataset with a natural coverage-based valuation function that increases with the inclusion of more relevant data points that would enhance responses to anticipated queries. Motivated by issues such as data control and prior-free revenue maximization, we focus on the scenario where each data point can be allocated to only one buyer. We show that the problem of welfare maximization in this setting is NP-hard even with two bidders, but design a polynomial-time approximation algorithm for any number of bidders. Unfortunately, however, this efficient allocation algorithm fails to be incentive compatible. The crux of our approach is a carefully tailored post-processing step called data burning which retains the approximation factor but achieves incentive compatibility. Our thorough experiments on synthetic and real-world image and text datasets demonstrate the practical effectiveness of our algorithm compared to popular baseline algorithms for combinatorial auctions.

Paper Structure

This paper contains 23 sections, 10 theorems, 37 equations, 1 figure, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Additional Discussion on Related Work
  3. Model and Problem Statement
  4. Public and Private Parameters:
  5. Bidding Setting and Objectives:
  6. Welfare Maximization: Computational Hardness and Approximation
  7. Incentive Compatible Welfare Maximization
  8. Experiments
  9. Useful Facts and Lemmas
  10. Omitted Proofs of Section \ref{['sec:new_algorithmic']}
  11. Proof of Proposition \ref{['th:demand_oracle_is_np_hard']}
  12. Proof of the First Claim in Theorem \ref{['thm:welfare-hard']}
  13. Proof of Second Claim in Theorem \ref{['thm:welfare-hard']}
  14. Proof of Lemma \ref{['lem:opt_lp']}
  15. Proof of Lemma \ref{['lem:rounding_approx']}
  16. ...and 8 more sections

Key Result

Proposition 3.2

The demand oracle cannot be implemented in polynomial time unless $P=NP$.

Figures (1)

  • Figure 1: Runtime in seconds of each algorithm.

Theorems & Definitions (32)

  • Definition 3.1
  • Proposition 3.2
  • Theorem 3.3
  • Lemma 3.4
  • Lemma 3.5
  • Theorem 3.6
  • Definition 4.1
  • Lemma 4.2
  • Theorem 4.4
  • Lemma 4.5
  • ...and 22 more