Approachability with delayed information

We consider a sequential decision problem where the decision maker is informed of the actual payoff with delay. We introduce a new condition, which generalizes the condition given by Blackwell and ensures that the decision maker can approach a fixed closed and convex set under delay. We show how the convergence rate to the approachable set is sensitive to changes in the information lag and apply our approachability strategy to games with one-sided incomplete information and to regret-free strategies.