A new strategy for Robbins' problem of optimal stopping
نویسندگان
چکیده
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 combining rank dependent rules with threshold rules. This rule attains an expected rank lower than the best upper bounds obtained in the literature so far, in particular we obtain an expected rank of 2.32614.
منابع مشابه
On Bayes Tests for p ~ i Versus p > i :
Few if any obtain a measure of success in their chosen profession without the beneficent influence of others. The first author is no exception. His interest in optimal stopping problems was ignited as a student in 1965 when Professor Robbins was visiting the University of Minnesota. Perhaps a fitting way of expressing appreciation would be to use this occasion to introduce the second author, Xi...
متن کاملRigorous Computer Analysis of the Chow-Robbins Game
Flip a coin repeatedly, and stop whenever you want. Your payoff is the proportion of heads, and you wish to maximize this payoff in expectation. This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded number crunching can show that it is best to continue in a given position, establishing rigorously that stopping is optimal seems at first sight to require “back...
متن کاملOptimal Stopping Policy for Multivariate Sequences a Generalized Best Choice Problem
In the classical versions of “Best Choice Problem”, the sequence of offers is a random sample from a single known distribution. We present an extension of this problem in which the sequential offers are random variables but from multiple independent distributions. Each distribution function represents a class of investment or offers. Offers appear without any specified order. The objective is...
متن کاملHalf-Prophets and Robbins’ Problem of Minimizing the Expected Rank
Let X1,X2, . . . ,Xn be i.i.d. random variables with a known continuous distribution function. Robbins’ problem is to find a sequential stopping rule without recall which minimizes the expected rank of the selected observation. An upper bound (obtained by memoryless threshold rules) and a procedure to obtain lower bounds of the value are known, but the essence of the problem is still unsolved. ...
متن کاملNew Optimal Observer Design Based on State Prediction for a Class of Non-linear Systems Through Approximation
This paper deals with the optimal state observer of non-linear systems based on a new strategy. Despite the development of state prediction in linear systems, state prediction for non-linear systems is still challenging. In this paper, to obtain a future estimation of the system states, initially Taylor series expansion of states in their receding horizons was achieved to any specified order an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Applied Probability
دوره 54 شماره
صفحات -
تاریخ انتشار 2017