Growth Rate Estimates for the Maximizer Sequence in an Adaptive Score‐Based Secretary Problem
Zeke Espinoza, Xin Yang Lu, Xiang Xu
Source abstract
ABSTRACT In [ Journal of Mathematical Study , 57 (2024): 476–485], the authors studied a sequence of expected score functions arising from an adaptive algorithm motivated by the classical score‐based secretary problem. More specifically, they proved that, for each , the corresponding expected score function admits a unique maximizer, and that the resulting sequence of maximizers is monotonically increasing and diverges to infinity as . In the present paper, we further investigate the asymptotic behavior of this maximizer sequence by establishing both upper and lower bounds for its growth rate.
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