Regularized contextual bandits

We consider the stochastic contextual bandit problem with additional regularization. The motivation comes from problems where the policy of the agent must be close to some baseline policy known to perform well on the task. To tackle this problem we use a nonparametric model and propose an algorithm splitting the context space into bins, solving simultaneously - and independently - regularized multi-armed bandit instances on each bin. We derive slow and fast rates of convergence, depending on the unknown complexity of the problem. We also consider a new relevant margin condition to get problem-independent convergence rates, yielding intermediate rates interpolating between the aforementioned slow and fast rates.