Arlotto, A; Steele, JM, Optimal Online Selection of an Alternating Subsequence: A Central Limit Theorem,
Advances in Applied Probability, vol. 46 no. 2
(June, 2014),
pp. 536-559, Cambridge University Press (CUP)
(last updated on 2023/06/01)
Abstract:
We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence ofnindependent observations from a continuous distributionF, 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.