Optimistic optimization of a Brownian
Document type :
Communication dans un congrès avec actes
Title :
Optimistic optimization of a Brownian
Author(s) :
Grill, Jean-Bastien [Auteur]
DeepMind [Paris]
Sequential Learning [SEQUEL]
Valko, Michal [Auteur]
Sequential Learning [SEQUEL]
Munos, Rémi [Auteur]
Sequential Learning [SEQUEL]
DeepMind [Paris]
DeepMind [Paris]
Sequential Learning [SEQUEL]
Valko, Michal [Auteur]

Sequential Learning [SEQUEL]
Munos, Rémi [Auteur]
Sequential Learning [SEQUEL]
DeepMind [Paris]
Conference title :
NeurIPS 2018 - Thirty-second Conference on Neural Information Processing Systems
City :
Montréal
Country :
Canada
Start date of the conference :
2018-12-02
HAL domain(s) :
Statistiques [stat]/Machine Learning [stat.ML]
English abstract : [en]
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 ε-approximation of its maximum using the ...
Show more >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 ε-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/ε). 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.Show less >
Show more >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 ε-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/ε). 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.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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