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We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection arising in the disciplines of…
This work investigates the optimal selection of the $m$th last success in a sequence of $n$ independent Bernoulli trials. We propose a threshold strategy that is $\varepsilon$-optimal under minimal assumptions about the monotonicity of the…
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
We consider the stochastic sequential assignment problem of Derman, Lieberman and Ross (1972) corresponding to a discrete distribution supported on a finite set of points. We use large deviation estimates to compute the asymptotics of the…
The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values…
This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record…
We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
In pure exploration problems, a statistician sequentially collects information to answer a question about some stochastic and unknown environment. The probability of returning a wrong answer should not exceed a maximum risk parameter…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
In this paper, it is shown that the solutions of general differentiable constrained optimization problems can be viewed as asymptotic solutions to sets of Ordinary Differential Equations (ODEs). The construction of the ODE associated to the…
Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the…
The well-known secretary problem in sequential analysis and optimal stopping theory asks one to maximize the probability of finding the optimal candidate in a sequentially examined list under the constraint that accept/reject decisions are…
In this paper we consider two variants of the Secretary problem: The Best-or-Worst and the Postdoc problems. We extend previous work by considering that the number of objects is not known and follows either a discrete Uniform distribution…
An asymptotically optimal sampling-based planner employs sampling to solve robot motion planning problems and returns paths with a cost that converges to the optimal solution cost, as the number of samples approaches infinity. This…
We consider the rigorous derivation of asymptotic formulas for initial-boundary value problems using the nonlinear steepest descent method. We give detailed derivations of the asymptotics in the similarity and self-similar sectors for the…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on…
We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only…