Contextual bandits with surrogate losses: Margin bounds and efficient algorithms

We use surrogate losses to obtain several new regret bounds and new algorithms for contextual bandit learning. Using the ramp loss, we derive new margin-based regret bounds in terms of standard sequential complexity measures of a benchmark class of real-valued regression functions. Using the hinge loss, we derive an efficient algorithm with a root dT-type mistake bound against benchmark policies induced by d-dimensional regressors. Under realizability assumptions, our results also yield classical regret bounds.