We propose a novel formal model for optimizing interactive information retrieval interfaces. To model interactive retrieval in a general way, we frame the task of an interactive retrieval system as to choose a sequence of interface cards to present to the user. At each interaction lap, the system's goal is to choose an interface card that can maximize the expected gain of relevant information for the user while minimizing the effort of the user with consideration of the user's action model and any desired constraints on the interface card. We show that such a formal interface card model can not only cover the Probability Ranking Principle for Interactive Information Retrieval as a special case by making multiple simplification assumptions, but also be used to derive a novel formal interface model for adaptively optimizing navigational interfaces in a retrieval system. Experimental results show that the proposed model is effective in automatically generating adaptive navigational interfaces, which outperform the baseline pre-designed static interfaces.