Related papers: Running minimum in the best-choice problem
Consider the problem of matching two independent i.i.d. samples of size $N$ from two distributions $P$ and $Q$ in $\mathbb{R}^d$. For an arbitrary continuous cost function, the optimal assignment problem looks for the matching that…
The classical Erd\H{o}s-Littlewood-Offord problem concerns the random variable $X = a_1 \xi_1 + \dots + a_n \xi_n$, where $a_i \in \mathbb{R} \setminus \{0\}$ are fixed and $\xi_i \sim \text{Ber}(1/2)$ are independent. The…
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…
We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
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…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
Poisson approximation using Stein's method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for…
This paper introduces a new class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is governed by an infinite horizon backward…
We provide algorithms that learn simple auctions whose revenue is approximately optimal in multi-item multi-bidder settings, for a wide range of valuations including unit-demand, additive, constrained additive, XOS, and subadditive. We…
The problem of statistical learning is to construct an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d. training sample from their joint distribution. Allowable predictors are…
The trade-off between the cost of acquiring and processing data, and uncertainty due to a lack of data is fundamental in machine learning. A basic instance of this trade-off is the problem of deciding when to make noisy and costly…
We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence…
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…
The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of…
We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the…
It is increasingly common to encounter time-varying random fields on networks (metabolic networks, sensor arrays, distributed computing, etc.). This paper considers the problem of optimal, nonlinear prediction of these fields, showing from…
We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…
We consider the question introduced by \cite{Mason2020} of identifying all the $\varepsilon$-optimal arms in a finite stochastic multi-armed bandit with Gaussian rewards. We give two lower bounds on the sample complexity of any algorithm…
Let $X_1, \ldots, X_n$ be independent random points drawn from an absolutely continuous probability measure with density $f$ in $\mathbb{R}^d$. Under mild conditions on $f$, we derive a Poisson limit theorem for the number of large…