@article{bubeck2015bandit,
author = {Bubeck, Sébastien and Dekel, Ofer and Koren, Tomer and Peres, Yuval},
title = {Bandit Convex Optimization: sqrt[T] Regret in One Dimension},
year = {2015},
month = {February},
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.},
url = {http://approjects.co.za/?big=en-us/research/publication/bandit-convex-optimization-sqrtt-regret-one-dimension/},
}