306 research outputs found
Prophet Inequalities with Limited Information
In the classical prophet inequality, a gambler observes a sequence of
stochastic rewards and must decide, for each reward ,
whether to keep it and stop the game or to forfeit the reward forever and
reveal the next value . The gambler's goal is to obtain a constant
fraction of the expected reward that the optimal offline algorithm would get.
Recently, prophet inequalities have been generalized to settings where the
gambler can choose items, and, more generally, where he can choose any
independent set in a matroid. However, all the existing algorithms require the
gambler to know the distribution from which the rewards are
drawn.
The assumption that the gambler knows the distribution from which
are drawn is very strong. Instead, we work with the much simpler
assumption that the gambler only knows a few samples from this distribution. We
construct the first single-sample prophet inequalities for many settings of
interest, whose guarantees all match the best possible asymptotically,
\emph{even with full knowledge of the distribution}. Specifically, we provide a
novel single-sample algorithm when the gambler can choose any elements
whose analysis is based on random walks with limited correlation. In addition,
we provide a black-box method for converting specific types of solutions to the
related \emph{secretary problem} to single-sample prophet inequalities, and
apply it to several existing algorithms. Finally, we provide a constant-sample
prophet inequality for constant-degree bipartite matchings.
We apply these results to design the first posted-price and multi-dimensional
auction mechanisms with limited information in settings with asymmetric
bidders
Show Me the Money: Dynamic Recommendations for Revenue Maximization
Recommender Systems (RS) play a vital role in applications such as e-commerce
and on-demand content streaming. Research on RS has mainly focused on the
customer perspective, i.e., accurate prediction of user preferences and
maximization of user utilities. As a result, most existing techniques are not
explicitly built for revenue maximization, the primary business goal of
enterprises. In this work, we explore and exploit a novel connection between RS
and the profitability of a business. As recommendations can be seen as an
information channel between a business and its customers, it is interesting and
important to investigate how to make strategic dynamic recommendations leading
to maximum possible revenue. To this end, we propose a novel \model that takes
into account a variety of factors including prices, valuations, saturation
effects, and competition amongst products. Under this model, we study the
problem of finding revenue-maximizing recommendation strategies over a finite
time horizon. We show that this problem is NP-hard, but approximation
guarantees can be obtained for a slightly relaxed version, by establishing an
elegant connection to matroid theory. Given the prohibitively high complexity
of the approximation algorithm, we also design intelligent heuristics for the
original problem. Finally, we conduct extensive experiments on two real and
synthetic datasets and demonstrate the efficiency, scalability, and
effectiveness our algorithms, and that they significantly outperform several
intuitive baselines.Comment: Conference version published in PVLDB 7(14). To be presented in the
VLDB Conference 2015, in Hawaii. This version gives a detailed submodularity
proo
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