In spoken dialogue systems, Partially Observable Markov Decision Processes (POMDPs) provide a formal framework for making dialogue management decisions under uncertainty, but efficiency and interpretability considerations mean that most current statistical dialogue managers are only MDPs. These MDP systems encode uncertainty explicitly in a single state representation. We formalise such MDP states in terms of distributions over POMDP states, and propose a new dialogue system architecture (Mixture Model POMDPs) which uses mixtures of these distributions to efficiently represent uncertainty. We also provide initial evaluation results (with real users) for this architecture. .
