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Randomized learning-augmented auctions with revenue guarantees

Ioannis Caragiannis, Georgios Kalantzis

TL;DR

This work investigates truthful single-item auctions when a machine-learned prediction for the highest valuation is available within a known range $[1,H]$. It introduces and analyzes randomized, anonymous “intuitive” auctions that allocate with positive probability only to the top bidders and satisfy a revenue guarantee relative to the top value, defined by consistency and robustness parameters. The authors prove a tight trade-off: a $\gamma$-consistent and $\rho$-robust DSIC intuitive auction exists if and only if $\gamma+\rho\cdot \ln{\max\{\hat{u}, H\rho/\gamma\}} \le 1$, and provide a constructive design achieving this bound. They further generalize robustness to depend on the prediction error via a function $\rho$, giving a necessary-and-sufficient condition involving $\rho(H/\hat{u})$ and two integrals, and present explicit $\rho$ forms yielding polylogarithmic or sublogarithmic dependence on error, including corollaries where robustness can be independent of $H$. Overall, the results yield constant-consistency auctions with robust revenue guarantees and extend to error-dependent robustness, significantly improving revenue guarantees over prior deterministic approaches in learning-augmented auction settings.

Abstract

We consider the fundamental problem of designing a truthful single-item auction with the challenging objective of extracting a large fraction of the highest agent valuation as revenue. Following a recent trend in algorithm design, we assume that the agent valuations belong to a known interval, and a (possibly erroneous) prediction for the highest valuation is available. Then, auction design aims for high consistency and robustness, meaning that, for appropriate pairs of values $γ$ and $ρ$, the extracted revenue should be at least a $γ$- or $ρ$-fraction of the highest valuation when the prediction is correct for the input instance or not. We characterize all pairs of parameters $γ$ and $ρ$ so that a randomized $γ$-consistent and $ρ$-robust auction exists. Furthermore, for the setting in which robustness can be a function of the prediction error, we give sufficient and necessary conditions for the existence of robust auctions and present randomized auctions that extract a revenue that is only a polylogarithmic (in terms of the prediction error) factor away from the highest agent valuation.

Randomized learning-augmented auctions with revenue guarantees

TL;DR

This work investigates truthful single-item auctions when a machine-learned prediction for the highest valuation is available within a known range . It introduces and analyzes randomized, anonymous “intuitive” auctions that allocate with positive probability only to the top bidders and satisfy a revenue guarantee relative to the top value, defined by consistency and robustness parameters. The authors prove a tight trade-off: a -consistent and -robust DSIC intuitive auction exists if and only if , and provide a constructive design achieving this bound. They further generalize robustness to depend on the prediction error via a function , giving a necessary-and-sufficient condition involving and two integrals, and present explicit forms yielding polylogarithmic or sublogarithmic dependence on error, including corollaries where robustness can be independent of . Overall, the results yield constant-consistency auctions with robust revenue guarantees and extend to error-dependent robustness, significantly improving revenue guarantees over prior deterministic approaches in learning-augmented auction settings.

Abstract

We consider the fundamental problem of designing a truthful single-item auction with the challenging objective of extracting a large fraction of the highest agent valuation as revenue. Following a recent trend in algorithm design, we assume that the agent valuations belong to a known interval, and a (possibly erroneous) prediction for the highest valuation is available. Then, auction design aims for high consistency and robustness, meaning that, for appropriate pairs of values and , the extracted revenue should be at least a - or -fraction of the highest valuation when the prediction is correct for the input instance or not. We characterize all pairs of parameters and so that a randomized -consistent and -robust auction exists. Furthermore, for the setting in which robustness can be a function of the prediction error, we give sufficient and necessary conditions for the existence of robust auctions and present randomized auctions that extract a revenue that is only a polylogarithmic (in terms of the prediction error) factor away from the highest agent valuation.
Paper Structure (12 sections, 5 theorems, 43 equations, 1 figure)

This paper contains 12 sections, 5 theorems, 43 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Our contribution
  3. Related work
  4. Preliminaries
  5. A consistency vs. robustness trade-off
  6. Proving the "if" part of Theorem \ref{['thm:single-bidder']}
  7. Proving the "only if" part of Theorem \ref{['thm:single-bidder']}
  8. Robustness as a function of prediction error
  9. Proving the "if" part of Theorem \ref{['thm:pred-error']}
  10. Proving the "only if" part of Theorem \ref{['thm:pred-error']}
  11. Applications of Theorem \ref{['thm:pred-error']}
  12. Conclusion

Key Result

Lemma 1

The allocation rule $\mathbf{x}$ is implementable if and only if it is monotone. If $\mathbf{x}$ is monotone, it is implementable through the payment rule $\mathbf{p}$, which, for every agent $i$ and any bids $\mathbf{b}_{-i}$ by the other agents, it holds $x_i(1,\mathbf{b}_{-i})\geq p_i(1,\mathbf{b for every $s,t\in [1,H]$ with $s\leq t$.

Figures (1)

  • Figure 1: The most general form of the allocation function $\bar{x}$ for an agent in terms of her valuation $t$, assuming $1<b<\widehat{u}<\frac{\gamma\cdot \widehat{u}}{\rho}<H$ and $\nu=1$. Notice that $\bar{x}(t,b,\nu)$ consists of five parts: the leftmost part in which the item is not allocated to the agent, the point corresponding to a tie for the highest bid, and three more parts in which the allocation function has logarithmic, constant, and again logarithmic form. The remaining cases for the relative values of $b$, $\widehat{u}$, $\frac{\gamma\cdot \widehat{u}}{\rho}$ and $H$ do not include some of the three rightmost parts. The black and white dots are used at points in which the allocation function "jumps"; the black dot represents the allocation value at these points.

Theorems & Definitions (7)

  • Lemma 1: Myerson's Lemma
  • Lemma 2
  • proof
  • Theorem 3
  • Theorem 4
  • Corollary 5
  • proof