English

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}
}