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Optimistic Optimization of a Brownian

2020-02-14 | |  58 |   30 |   0

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 image.png-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 log2 (1/image.png). 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.

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