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An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu
An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu
OUR Journal: ODU Undergraduate Research Journal
This paper presents an alternate proof of the divergence of the unique maximizer sequence {π₯β π} of a function sequence {πΉπ(π₯)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here βthe secretary problemβ. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {ππ,π π } and relies on the strict monotonicity of πΉπ(π₯) as π increases in order to show divergence of {π₯β π}. Towards this, limits of the exponentiated Gaussian CDF are β¦