Online learning in adversarial lipschitz environments
Odalric-Ambrym Maillard and Rémi Munos
In: ECML 2010, Barcelone(2010).
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 O(sqrt dT ln(lambda)) where d is the dimension of the search space, T the time horizon, and lambda 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.