Minimax regret with imperfect ex-post knowledge of the state

We consider decision problems under complete ignorance and extend the minimax regret principle to situations where, after taking an action, the decision maker does not necessarily learn the state of the world. For example, if the decision maker only learns what the outcome is, then all she knows is that the actual state is one of the possibly several states that yield the observed outcome under the chosen action. We refer to this situation as imperfect ex-post information. We also extend the framework to encompass the possibility of less than the extreme pessimism that characterizes the minimax regret criterion.