PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Online Learning in Adversarial Lipschitz Environments
Odalric-Ambrym Maillard and Rémi Munos
European conference on Machine learning and knowledge discovery in databases Volume 2, Number 2010, pp. 305-320, 2010.

Abstract

We consider the problem of online learning in an adversarial environment when the reward functions chosen by the adversary are assumed to be Lipschitz. This setting extends previous works on linear and convex online learning. We provide a class of algorithms with cumulative regret upper bounded by \tildeO(\sqrt{dT ln(λ)}) where d is the dimension of the search space, T the time horizon, and λ the Lipschitz constant. Efficient numerical implementations using particle methods are discussed. Applications include online supervised learning problems for both full and partial (bandit) information settings, for a large class of non-linear regressors/classifiers, such as neural networks.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:7521
Deposited By:Odalric-Ambrym Maillard
Deposited On:17 March 2011