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- W4288633277 abstract "We address the problem of optimizing a Brownian motion. We consider a (random) realization $W$ of a Brownian motion with input space in $[0,1]$. Given $W$, our goal is to return an $epsilon$-approximation of its maximum using the smallest possible number of function evaluations, the sample complexity of the algorithm. We provide an algorithm with sample complexity of order $log^2(1/epsilon)$. This improves over previous results of Al-Mharmah and Calvin (1996) and Calvin et al. (2017) which provided only polynomial rates. Our algorithm is adaptive---each query depends on previous values---and is an instance of the optimism-in-the-face-of-uncertainty principle." @default.
- W4288633277 created "2022-07-30" @default.
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- W4288633277 date "2018-12-02" @default.
- W4288633277 modified "2023-09-25" @default.
- W4288633277 title "Optimistic optimization of a Brownian" @default.
- W4288633277 hasPublicationYear "2018" @default.
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