On-Line Selection of Alternating Subsequences from a Random Sample

TL;DR

This paper analyzes the optimal strategy for sequentially selecting alternating subsequences from i.i.d. continuous random variables, revealing that constrained decision-makers perform only slightly worse than those with full knowledge.

Contribution

It provides the exact asymptotic behavior of the optimal sequential selection process and quantifies the performance gap between constrained and unconstrained decision-makers.

Findings

Optimal asymptotic behavior characterized

Sequential selection incurs about 12% performance loss

Performance gap between constrained and full-knowledge selection

Abstract

We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected subsequence. Moreover, we find (in a sense we make precise) that a person who is constrained to make sequential selections does only about 12% worse than a person who can make selections with full knowledge of the random sequence.