@inproceedings{20939c9f280441fbade4e660d9f7831a,

title = "Bandit convex optimization: √T regret in one dimension",

abstract = "We analyze the minimax regret of the adversarial bandit convex optimization problem. Focusing on the one-dimensional case, we prove that the minimax regret is θ∼(√T) and partially resolve a decade-old open problem. Our analysis is non-constructive, as we do not present a concrete algorithm that attains this regret rate. Instead, we use minimax duality to reduce the problem to a Bayesian setting, where the convex loss functions are drawn from a worst-case distribution, and then we solve the Bayesian version of the problem with a variant of Thompson Sampling. Our analysis features a novel use of convexity, formalized as a {"}local-to-global{"} property of convex functions, that may be of independent interest.",

author = "S{\'e}bastien Bubeck and Ofer Dekel and Tomer Koren and Yuval Peres",

note = "Publisher Copyright: {\textcopyright} 2015 A. Agarwal & S. Agarwal.; 28th Conference on Learning Theory, COLT 2015 ; Conference date: 02-07-2015 Through 06-07-2015",

year = "2015",

language = "الإنجليزيّة",

volume = "40",

series = "Proceedings of Machine Learning Research",

publisher = "PMLR",

editor = "Peter Gr{\"u}nwald and Elad Hazan and Satyen Kale",

booktitle = "Proceedings of The 28th Conference on Learning Theory",

edition = "2015",

}