Asymptotics of the optimum in discrete sequential assignment

TL;DR

This paper analyzes the asymptotic behavior of the optimal policy in a discrete sequential assignment problem using large deviation estimates, providing insights into its performance as the number of tasks grows large.

Contribution

It introduces a large deviation approach to determine the asymptotics of the optimal policy in a finite-support discrete sequential assignment problem.

Findings

Asymptotic formulas for the optimal policy as N approaches infinity

Application of large deviation estimates to sequential assignment

Enhanced understanding of policy performance in large-scale problems

Abstract

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 optimal policy as the number of tasks $N \to \infty$.