Stochastic Bandits with Pathwise Constraints

We consider the problem of stochastic bandits, with the goal of maximizing a reward while satisfying pathwise constraints. The motivation for this problem comes from cognitive radio networks, in which agents need to choose between different transmission profiles to maximize throughput under certain operational constraints such as limited average power. Stochastic bandits serve as a natural model for an unknown, stationary environment. We propose an algorithm, based on a steering approach, and analyze its regret with respect to the optimal stationary policy that knows the statistics of the different arms.