Optimal Single-Choice Prophet Inequalities from Samples

We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single sample from each distribution. When the distributions are identical, we show that for any constant $\varepsilon > 0$, $O(n)$ samples from the distribution suffice to achieve the optimal competitive ratio ($\approx 0.745$) within $(1+\varepsilon)$, resolving an open problem of Correa, D\"utting, Fischer, and Schewior.Comment: Appears in Innovations in Theoretical Computer Science (ITCS) 202

Learning Reserve Prices in Second-Price Auctions

This paper proves the tight sample complexity of Second-Price Auction with Anonymous Reserve, up to a logarithmic factor, for each of all the value distribution families studied in the literature: [0,1]-bounded, [1,H]-bounded, regular, and monotone hazard rate (MHR). Remarkably, the setting-specific tight sample complexity poly(?^{-1}) depends on the precision ? ? (0, 1), but not on the number of bidders n ? 1. Further, in the two bounded-support settings, our learning algorithm allows correlated value distributions. In contrast, the tight sample complexity ??(n) ? poly(?^{-1}) of Myerson Auction proved by Guo, Huang and Zhang (STOC 2019) has a nearly-linear dependence on n ? 1, and holds only for independent value distributions in every setting. We follow a similar framework as the Guo-Huang-Zhang work, but replace their information theoretical arguments with a direct proof

Learning Reserve Prices in Second-Price Auctions

This paper proves the tight sample complexity of Second-Price Auction with Anonymous Reserve, up to a logarithmic factor, for all value distribution families that have been considered in the literature. Compared to Myerson Auction, whose sample complexity was settled very recently in (Guo, Huang and Zhang, STOC 2019), Anonymous Reserve requires much fewer samples for learning. We follow a similar framework as the Guo-Huang-Zhang work, but replace their information theoretical argument with a direct proof

Developments in Multi-Agent Fair Allocation

Fairness is becoming an increasingly important concern when designing markets, allocation procedures, and computer systems. I survey some recent developments in the field of multi-agent fair allocation