Related papers: Variable Decomposition for Prophet Inequalities an…
We introduce the \textit{prophet inequality with uncertain acceptance} model, in which a decision maker sequentially observes a sequence of independent options, each characterized by a value $x_i$ and an acceptance probability $p_i$, both…
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…
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 this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…
We consider prophet inequalities under downward-closed constraints. In this problem, a decision-maker makes immediate and irrevocable choices on arriving elements, subject to constraints. Traditionally, performance is compared to the…
Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…
Consider a gambler who observes a sequence of independent, non-negative random numbers and is allowed to stop the sequence at any time, claiming a reward equal to the most recent observation. The famous prophet inequality of Krengel,…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
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…
We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et…
Hypothesis Selection is a fundamental distribution learning problem where given a comparator-class $Q=\{q_1,\ldots, q_n\}$ of distributions, and a sampling access to an unknown target distribution $p$, the goal is to output a distribution…
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…
We consider prophet inequalities subject to feasibility constraints that are the intersection of $q$ matroids. The best-known algorithms achieve a $\Theta(q)$-approximation, even when restricted to instances that are the intersection of $q$…
We study a continuous and infinite time horizon counterpart to the classic prophet inequality, which we term the stationary prophet inequality problem. Here, copies of a good arrive and perish according to Poisson point processes. Buyers…
There are two major models of value uncertainty in the optimal stopping literature: the secretary model, which assumes no prior knowledge, and the prophet inequality model, which assumes full information about value distributions. In…
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…
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…
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…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…