Related papers: Prophet Secretary Through Blind Strategies
The setting of the classic prophet inequality is as follows: a gambler is shown the probability distributions of $n$ independent, non-negative random variables with finite expectations. In their indexed order, a value is drawn from each…
In a prophet inequality problem, $n$ independent random variables are presented to a gambler one by one. The gambler decides when to stop the sequence and obtains the most recent value as reward. We evaluate a stopping rule by the…
Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps…
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…
In this work, we study the single-choice prophet inequality problem, where a gambler faces a sequence of~$n$ online i.i.d. random variables drawn from an unknown distribution. When a variable reveals its value, the gambler needs to decide…
The classical Prophet Inequality arises from a fundamental problem in optimal-stopping theory. In this problem, a gambler sees a finite sequence of independent, non-negative random variables. If he stops the sequence at any time, he…
Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values in an online fashion, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on…
In the prophet inequality problem, a gambler faces a sequence of items arriving online with values drawn independently from known distributions. On seeing an item, the gambler must choose whether to accept its value as her reward and quit…
The prophet secretary problem is a combination of the prophet inequality and the secretary problem, where elements are drawn from known independent distributions and arrive in uniformly random order. In this work, we design 1) a…
Prophet inequalities are a central object of study in optimal stopping theory. In the iid model, a gambler sees values in an online fashion, sampled independently from a given distribution. Upon observing each value, the gambler either…
In the classical prophet inequality, a gambler observes a sequence of stochastic rewards $V_1,...,V_n$ and must decide, for each reward $V_i$, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value…
Free order prophet inequalities bound the ratio between the expected value obtained by two parties each selecting a value from a set of independent random variables: a "prophet" who knows the value of each variable and may select the…
In this paper, we introduce an over-time variant of the well-known prophet inequality with i.i.d. random variables. Instead of stopping with one realized value at some point in the process, we decide for each step how long we select the…
The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. We consider a variant of the problem and explore its connections to data-driven…
In the prophet secretary problem, $n$ values are drawn independently from known distributions, and presented in a uniformly random order. A decision-maker must accept or reject each value when it is presented, and may accept at most $k$…
In the classical prophet inequality, a gambler faces a sequence of items, whose values are drawn independently from known distributions. Upon the arrival of each item, its value is realized and the gambler either accepts it and the game…
Many online problems are studied in stochastic settings for which inputs are samples from a known distribution, given in advance, or from an unknown distribution. Such distributions model both beyond-worst-case inputs and, when given,…
Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight $\frac{1}{2}$-approximation to the…
Suppose a customer is faced with a sequence of fluctuating prices, such as for airfare or a product sold by a large online retailer. Given distributional information about what price they might face each day, how should they choose when to…
Prophet inequalities compare online stopping strategies against an omniscient "prophet" using distributional knowledge. In this work, we augment this model with a conservative prediction of the maximum realized value. We quantify the…