@inproceedings{bubeck2015multi-scale,
author = {Bubeck, Sébastien and Eldan, Ronen},
title = {Multi-Scale Exploration of Convex Functions and Bandit Convex Optimization},
booktitle = {arXiv:1507.06580v1 [math.MG]},
year = {2015},
month = {July},
abstract = {We construct a new map from a convex function to a distribution on its domain, with the property that this distribution is a multi-scale exploration of the function. We use this map to solve a decade-old open problem in adversarial bandit convex optimization by showing that the minimax regret for this problem is O~(poly(n)T√) , where n is the dimension and T the number of rounds. This bound is obtained by studying the dual Bayesian maximin regret via the information ratio analysis of Russo and Van Roy, and then using the multi-scale exploration to solve the Bayesian problem.},
url = {http://approjects.co.za/?big=en-us/research/publication/multi-scale-exploration-convex-functions-bandit-convex-optimization/},
edition = {arXiv:1507.06580v1 [math.MG]},
note = {Best Paper Award},
}