Targeting a simple statistical bandit problem

This manuscript deals with the estimation of the optimal rule and its meanreward in a simple bandit setting where, at each round, the player is given acontext, chooses one of two actions based on the context and all pastobservations, and receives a reward corresponding to the action undertaken.The player focuses on the mean reward and tries to narrow her confidenceinterval for it, but it happens that she can also estimate her regret.Inference hinges on the targeted learning methodology. A simulation studyillustrates the results of the manuscript