Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
The weighted majority algorithm
Information and Computation
Characterizations of learnability for classes of {0, …, n}-valued functions
Journal of Computer and System Sciences
Journal of the ACM (JACM)
Scale-sensitive dimensions, uniform convergence, and learnability
Journal of the ACM (JACM)
A game of prediction with expert advice
Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
The Nonstochastic Multiarmed Bandit Problem
SIAM Journal on Computing
On Learning Sets and Functions
Machine Learning
Ultraconservative online algorithms for multiclass problems
The Journal of Machine Learning Research
Using confidence bounds for exploitation-exploration trade-offs
The Journal of Machine Learning Research
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Prediction, Learning, and Games
Prediction, Learning, and Games
Pattern Recognition for Conditionally Independent Data
The Journal of Machine Learning Research
Efficient bandit algorithms for online multiclass prediction
Proceedings of the 25th international conference on Machine learning
Robust bounds for classification via selective sampling
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Generalization error bounds using unlabeled data
COLT'05 Proceedings of the 18th annual conference on Learning Theory
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Most of the research in online learning is focused either on the problem of adversarial classification (i.e., both inputs and labels are arbitrarily chosen by an adversary) or on the traditional supervised learning problem in which samples are independent and identically distributed according to a stationary probability distribution. Nonetheless, in a number of domains the relationship between inputs and outputs may be adversarial, whereas input instances are i.i.d. from a stationary distribution (e.g., user preferences). This scenario can be formalized as a learning problem with stochastic inputs and adversarial outputs. In this paper, we introduce this novel stochastic-adversarial learning setting and we analyze its learnability. In particular, we show that in a binary classification problem over a horizon of n rounds, given a hypothesis space H with finite VC-dimension, it is possible to design an algorithm that incrementally builds a suitable finite set of hypotheses from H used as input for an exponentially weighted forecaster and achieves a cumulative regret of order O(nVC(H)logn) with overwhelming probability. This result shows that whenever inputs are i.i.d. it is possible to solve any binary classification problem using a finite VC-dimension hypothesis space with a sub-linear regret independently from the way labels are generated (either stochastic or adversarial). We also discuss extensions to multi-class classification, regression, learning from experts and bandit settings with stochastic side information, and application to games.