Optimal Online Selection of an Alternating Subsequence: A Central Limit Theorem
Alessandro Arlotto, J. Michael Steele · Advances in Applied Probability · 2014
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.