Related papers: IID Prophet Inequality with Random Horizon: Going …
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…
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…
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 our problem, we are given access to a number of sequences of nonnegative i.i.d. random variables, whose realizations are observed sequentially. All sequences are of the same finite length. The goal is to pick one element from each…
The prophet inequality is one of the cornerstone problems in optimal stopping theory and has become a crucial tool for designing sequential algorithms in Bayesian settings. In the i.i.d. $k$-selection prophet inequality problem, we…
This work addresses the classic machine learning problem of online prediction with expert advice. A new potential-based framework for the fixed horizon version of this problem has been recently developed using verification arguments from…
We study the Improving Multi-Armed Bandit (IMAB) problem, where the reward obtained from an arm increases with the number of pulls it receives. This model provides an elegant abstraction for many real-world problems in domains such as…
We study a fundamental problem in optimization under uncertainty. There are $n$ boxes; each box $i$ contains a hidden reward $x_i$. Rewards are drawn i.i.d. from an unknown distribution $\mathcal{D}$. For each box $i$, we see $y_i$, an…
The rich literature on online Bayesian selection problems has long focused on so-called prophet inequalities, which compare the gain of an online algorithm to that of a "prophet" who knows the future. An equally-natural, though…
The prophet inequalities problem has received significant study over the past decades and has several applications such as to online auctions. In this paper, we study two variants of the i.i.d. prophet inequalities problem, namely the…
We study the repeated optimal stopping problem, in which the same optimal stopping instance with an unknown distribution is solved repeatedly over $T$ rounds. We aim to simultaneously achieve strong per-round performance guarantees relative…
The Prophet Inequality and Pandora's Box problems are fundamental stochastic problem with applications in Mechanism Design, Online Algorithms, Stochastic Optimization, Optimal Stopping, and Operations Research. A usual assumption in these…
Suppose $X_1,X_2,...$ are i.i.d. nonnegative random variables with finite expectation, and for each $k$, $X_k$ is observed at the $k$-th arrival time $S_k$ of a Poisson process with unit rate which is independent of the sequence $\{X_k\}$.…
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 Bayesian online settings, every element has a value that is drawn from a known underlying distribution, which we refer to as the element's identity. The elements arrive sequentially. Upon the arrival of an element, its value is revealed,…
Competition complexity formalizes a compelling intuition: rather than refining the mechanism, how much additional competition is sufficient for a simple mechanism to compete with an optimal one? We begin the study of this question in…
Consider a stream of $n$ random points (say, from the unit square) arriving one by one, where a player has to make an irreversible immediate decision for each arriving point whether to pick it. The player has to pick a single point, and the…
In the classical optimal stopping problem, a player is given a sequence of random variables $X_1\ldots X_n$ with known distributions. After observing the realization of $X_i$, the player can either accept the observed reward from $X_i$ and…
Prophet inequalities and secretary problems have been extensively studied in recent years due to their elegance, connections to online algorithms, stochastic optimization, and mechanism design problems in game theoretic settings. Rubinstein…
Prophet inequalities compare the expected performance of an online algorithm for a stochastic optimization problem to the expected optimal solution in hindsight. They are a major alternative to classic worst-case competitive analysis, of…