Prophet Secretary: Surpassing the 1-1/e Barrier
نویسندگان
چکیده
In the Prophet Secretary problem, samples from a known set of probability distributions arrive one by one in a uniformly random order, and an algorithm must irrevocably pick one of the samples as soon as it arrives. The goal is to maximize the expected value of the sample picked relative to the expected maximum of the distributions. This is one of the most simple and fundamental problems in online decision making that models the process selling one item to a sequence of costumers. For a closely related problem called the Prophet Inequality where the order of the random variables is adversarial, it is known that one can achieve in expectation 1/2 of the expected maximum, and no better ratio is possible. For the Prophet Secretary problem, that is, when the variables arrive in a random order, Esfandiari et al. [7] showed that one can actually get 1− 1/e of the maximum. The 1− 1/e bound was recently extended to more general settings [6]. Given these results, one might be tempted to believe that 1 − 1/e is the correct bound. We show that this is not the case by providing an algorithm for the Prophet Secretary problem that beats the 1− 1/e bound and achieves 1− 1/e+ 1/400 of the optimum value. We also prove a hardness result on the performance of algorithms under a natural restriction which we call deterministic distribution-insensitivity.
منابع مشابه
Prophet Secretary for Combinatorial Auctions and Matroids
The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most important of these generalizations are to matroids and to combinatorial auctions (extends bipartite matching). Kleinberg-Weinberg [KW12] and Feldman et al. ...
متن کاملProphet Inequalities with Limited Information
In the classical prophet inequality, a gambler observes a sequence of stochastic rewards V1, ..., Vn and must decide, for each reward Vi, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value Vi. 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 be...
متن کاملCombinatorial Prophet Inequalities
We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an O(1)-competitive algorithm. For a monotone subadditive objective function over an arbitrary downward-closed feasibility constraint, we give an O(log n log r)-competitive algorithm (where r is...
متن کاملAdvances on Matroid Secretary Problems: Free Order Model and Laminar Case
The most important open conjecture in the context of the matroid secretary problem claims the existence of an O(1)-competitive algorithm applicable to any matroid. Whereas this conjecture remains open, modified forms of it have been shown to be true, when assuming that the assignment of weights to the secretaries is not adversarial but uniformly at random [23, 20]. However, so far, no variant o...
متن کاملAutomated Online Mechanism Design and Prophet Inequalities
Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the mechanism designer has no knowledge of the distribution of bid values. However, in many real-worl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1711.01834 شماره
صفحات -
تاریخ انتشار 2017