Randomized learning-augmented auctions with revenue guarantees

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.