Polynomial Cost of Adaptation for X -Armed Bandits
Machine Learning
2019-12-10 v2 Machine Learning
Statistics Theory
Statistics Theory
Abstract
In the context of stochastic continuum-armed bandits, we present an algorithm that adapts to the unknown smoothness of the objective function. We exhibit and compute a polynomial cost of adaptation to the H{\"o}lder regularity for regret minimization. To do this, we first reconsider the recent lower bound of Locatelli and Carpentier [20], and define and characterize admissible rate functions. Our new algorithm matches any of these minimal rate functions. We provide a finite-time analysis and a thorough discussion about asymptotic optimality.
Keywords
Cite
@article{arxiv.1905.10221,
title = {Polynomial Cost of Adaptation for X -Armed Bandits},
author = {Hédi Hadiji},
journal= {arXiv preprint arXiv:1905.10221},
year = {2019}
}