The weighted majority algorithm
Information and Computation
Journal of the ACM (JACM)
The Nonstochastic Multiarmed Bandit Problem
SIAM Journal on Computing
Adaptive and Self-Confident On-Line Learning Algorithms
COLT '00 Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
Gambling in a rigged casino: The adversarial multi-armed bandit problem
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Using confidence bounds for exploitation-exploration trade-offs
The Journal of Machine Learning Research
Online convex optimization in the bandit setting: gradient descent without a gradient
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Prediction, Learning, and Games
Prediction, Learning, and Games
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Nonstochastic bandits: Countable decision set, unbounded costs and reactive environments
Theoretical Computer Science
Multi-armed bandits in metric spaces
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Efficient bandit algorithms for online multiclass prediction
Proceedings of the 25th international conference on Machine learning
Logarithmic regret algorithms for online convex optimization
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Ranked bandits in metric spaces: learning diverse rankings over large document collections
The Journal of Machine Learning Research
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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 Õ(√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.