  We introduce a new stochastic smoothing perspective to study adversarial
contextual bandit problems. We propose a general algorithm template that
represents random perturbation based algorithms and identify several
perturbation distributions that lead to strong regret bounds. Using the idea of
smoothness, we provide an $O(\sqrt{T})$ zero-order bound for the vanilla
algorithm and an $O(L^{*2/3}_{T})$ first-order bound for the clipped version.
These bounds hold when the algorithms use with a variety of distributions that
have a bounded hazard rate. Our algorithm template includes EXP4 as a special
case corresponding to the Gumbel perturbation. Our regret bounds match existing
results for EXP4 without relying on the specific properties of the algorithm.
