Related papers: Single-Sample Prophet Inequalities via Greedy-Orde…
The study of the prophet inequality problem in the limited information regime was initiated by Azar et al. [SODA'14] in the pursuit of prior-independent posted-price mechanisms. As they show, $O(1)$-competitive policies are achievable using…
We study matroid prophet inequalities when distributions are unknown and accessible only through samples. While single-sample prophet inequalities for special matroids are known, no constant-factor competitive algorithm with even a…
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…
We consider the prophet inequality problem for (not necessarily bipartite) matching problems with independent edge values, under both edge arrivals and vertex arrivals. We show constant-factor prophet inequalities for the case where the…
We study a variant of the single-choice prophet inequality problem where the decision-maker does not know the underlying distribution and has only access to a set of samples from the distributions. Rubinstein et al. [2020] showed that the…
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…
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 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…
We study the prophet secretary problem, a well-studied variant of the classic prophet inequality, where values are drawn from independent known distributions but arrive in uniformly random order. Upon seeing a value at each step, 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…
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…
We take a unifying approach to single selection optimal stopping problems with random arrival order and independent sampling of items. In the problem we consider, a decision maker (DM) initially gets to sample each of $N$ items…
We introduce a variant of the classic prophet inequality, called \emph{residual prophet inequality} (RPI). In the RPI problem, we consider a finite sequence of $n$ nonnegative independent random values with known distributions, and a known…
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…
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…
In modern sample-driven Prophet Inequality, an adversary chooses a sequence of $n$ items with values $v_1, v_2, \ldots, v_n$ to be presented to a decision maker (DM). The process follows in two phases. In the first phase (sampling phase),…
Due to their numerous applications, in particular in Mechanism Design, Prophet Inequalities have experienced a surge of interest. They describe competitive ratios for basic stopping time problems where random variables get revealed…
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…
In the classic prophet inequality, samples from independent random variables arrive online. A gambler that knows the distributions must decide at each point in time whether to stop and pick the current sample or to continue and lose that…
We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the $(1-\varepsilon)$-competition complexity of different types of online algorithms. This metric asks for the smallest…