Optimal On-Line Selection of an Alternating Subsequence: A Central Limit Theorem

TL;DR

This paper studies the optimal online strategy for selecting an alternating subsequence from independent observations and proves a central limit theorem for the number of selections, using dynamic programming techniques.

Contribution

It introduces a detailed analysis of the optimal policy for sequentially selecting an alternating subsequence and establishes a central limit theorem for the number of selections.

Findings

Proves a central limit theorem for the number of selected elements.

Analyzes the dynamic programming recursion of the selection process.

Provides a detailed understanding of the value functions and selection rules.

Abstract

We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of $n$ independent observations from a continuous distribution $F$, and we prove a central limit theorem for the number of selections made by that policy. The proof exploits the backward recursion of dynamic programming and assembles a detailed understanding of the associated value functions and selection rules.