We consider the problem of displaying advertise- ments on web pages in the "cost per click" model, which necessitates to learn the appeal of visitors for the different advertisements in order to maximize the revenue. In a realistic context, the advertisements have constraints such as a certain number of clicks to draw, as well as a lifetime. This problem is thus inherently dynamic, and intimately combines combinatorial and statistical issues. To set the stage, it is also noteworthy that we deal with very rare events of interest, since the base probability of one click is in the order of 10−4 . We introduce an adaptive policy learning algorithm based on linear programming, and investigate its performance through simulations on a realistic model designed with an important commercial web actor.