An Asymptotic Analysis on Generalized Secretary Problem
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As a famous result, the “37% Law” for Secretary Problem has widely influenced peoples' perception on online decision strategies about choice. However, using this strategy, too many attractive candidates may be rejected in the first 37%, and in practice people also tend to stop earlier<cit.>. In this paper, we argued that in most cases, the best-only optimization does not obtain an optimal outcome, while the optimal cutoff should be O(√(n)). And we also showed that in some strict objective that only cares several best candidates, Θ(n) skips are still needed.
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