Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice
Machine Learning
2015-11-09 v1 Machine Learning
Abstract
We prove non-asymptotic lower bounds on the expectation of the maximum of independent Gaussian variables and the expectation of the maximum of independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (asymptotically optimal) non-asymptotic lower bound on the minimax regret of online learning with expert advice.
Cite
@article{arxiv.1511.02176,
title = {Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice},
author = {Francesco Orabona and David Pal},
journal= {arXiv preprint arXiv:1511.02176},
year = {2015}
}