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

Alessandro Arlotto, J. Michael Steele

Published 2012-12-06, updated 2013-06-09Version 3

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.