Related papers: Sum the Probabilities to $m$ and Stop

This paper considers online optimization for a system that performs a sequence of back-to-back tasks. Each task can be processed in one of multiple processing modes that affect the duration of the task, the reward earned, and an additional…

Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…

A result of Chebyshev (1864) and Hoeffding1956}, on bounding an expectation of a given function with respect to a Bernoulli convolution (also called Poisson binomial law, or law of the number of successes in independent trials) with any…

We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of…

We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…

While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample…

In this article we study the expected rank problem under full information. Our approach uses the planar Poisson approach from Gnedin (2007) to derive the expected rank of a stopping rule that is one of the simplest non-trivial examples…

We study a generalization of the multi-armed bandit problem with multiple plays where there is a cost associated with pulling each arm and the agent has a budget at each time that dictates how much she can expect to spend. We derive an…

Consider the problem: we are given $n$ boxes, labeled $\{1,2,\ldots, n\}$ by an adversary, each containing a single number chosen from an unknown distribution; these $n$ distributions are not necessarily identical. We are also given an…

Given $n$ elements, an integer $k$ and a parameter $\varepsilon$, we study to select an element with rank in $(k-n\varepsilon,k+n\varepsilon]$ using unreliable comparisons where the outcome of each comparison is incorrect independently with…

We consider two variations of the classical secretary problem. * A variation of the returning secretary problem where each interviewee may appear a second time with a fixed probability p. The decision-maker observes interviewees…

We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…

We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution $D$. The seller has "data"' about $D$ in the form of $m \ge 1$ i.i.d. samples, and the algorithmic challenge is to use these…

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $\delta$, the so called refraction period. This prevents the optimal exercise times…

We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch…

A general result on the method of randomized stopping is proved. It is applied to optimal stopping of controlled diffusion processes with unbounded coefficients to reduce it to an optimal control problem without stopping. This is motivated…

A new thresholding method, based on L-statistics and called order thresholding, is proposed as a technique for improving the power when testing against high-dimensional alternatives. The new method allows great flexibility in the choice of…

In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being known in general scaling regimes for the noiseless setting.…

In a compound decision problem, consisting of $n$ statistically independent copies of the same problem to be solved under the sum of the individual losses, any reasonable compound decision rule $\delta$ satisfies a natural symmetry…

We give a conditional result on the constant in the B\'aez-Duarte reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We show that assuming the Riemann hypothesis and that $\sum_{\rho}\frac{1}{|\zeta'(\rho)|^2}\ll…