628 research outputs found
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
can be achieved with a single sample from each distribution. When the
distributions are identical, we show that for any constant ,
samples from the distribution suffice to achieve the optimal competitive
ratio () within , 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
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