In the context of Active Learning for classification, the classification error depends on the joint distribution of samples and their labels which is initially unknown. The minimization of this error requires estimating this distribution. Online estimation of this distribution involves a trade-off between exploration and exploitation. This is a common problem in machine learning for which multi-armed bandit theory, building upon Optimism in the Face of Uncertainty, has been proven very efficient these last years. We introduce two novel algorithms that use Optimism in the Face of Uncertainty along with Gaussian Processes for the Active Learning problem. The evaluation lead on real world datasets shows that these new algorithms compare positively to state-of-the-art methods.