Multi-scale exploration of convex functions and bandit convex optimization

  title={Multi-scale exploration of convex functions and bandit convex optimization},
  author={S{\'e}bastien Bubeck and Ronen Eldan},
We construct a new map from a convex function to a distributio n on its domain, with the property that this distribution is a multi-scale explorati on of the function. We use this map to solve a decade-old open problem in adversarial bandit conve x optimization by showing that the minimax regret for this problem is̃ O(poly(n) √ T ), wheren is the dimension andT the number of rounds. This bound is obtained by studying the dual Bayesian maximin regret via the information ratio analysis of Russo… CONTINUE READING
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Bandit convex opt imization

Bubeck, O. Dekel, T. Koren, Y. Peres
Annual Conference on Learning Theor y (COLT), • 2012

Regret analysis of stochastic and nonstochastic multiarmed bandit problems

S. Bubeck, N. Cesa-Bianchi
Foundations and Trends in Machine Learning • 2012

Multi - scale exploration of convex functions and bandit convex optimization

S. Bubeck, R. Eldan
Arxiv preprint arXiv

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