All the reviewers agree that the paper contributes novel results on the role of perturbations in multi armed bandit problems, of both the adversarial and stochastic varieties. Specifically, it provides a unified, Follow-the-Perturbed-Leader viewpoint for studying different perturbation based approaches to bandits, and as a byproduct shows new and well-performing variations of standard algorithms such as UCB. This is likely to be of interest in the theoretical design of online learning algorithms, and its ideas can be potentially extended to more complicated bandit settings with structure.