An adaptive \(O(\log n)\)-optimal policy for the online selection of a monotone subsequence from a random sample
Given a sequence of \(n\) independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such a policy is within \(O(\log n)\) of o...
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| Veröffentlicht in: | arXiv.org 2016-12 |
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| creator | Arlotto, Alessandro Wei, Yehua Xie, Xinchang |
| description | Given a sequence of \(n\) independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such a policy is within \(O(\log n)\) of optimal. Our construction provides a direct and natural way for proving the \(O(\log n)\)-optimality gap. An earlier proof of the same result made crucial use of a key inequality of Bruss and Delbaen (2001) and of de-Poissonization. |
| doi_str_mv | 10.48550/arxiv.1605.03998 |
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| subjects | Continuity (mathematics) Independent variables Optimization Random variables |
| title | An adaptive \(O(\log n)\)-optimal policy for the online selection of a monotone subsequence from a random sample |
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