Reasoning about Deterministic Actions with Probabilistic Prior and Application to Stochastic Filtering

We present a novel algorithm and a new understanding of reasoning about a sequence of deterministic actions with a probabilistic prior. When the initial state of a dynamic system is unknown, a probability distribution can be still specified over the initial states. Estimating the posterior distribution over states (filtering) after some deterministic actions occurred is a problem relevant to AI planning, natural language processing (NLP), and robotics among others. Current approaches to filtering deterministic actions are not tractable even if the distribution over the initial system state is represented compactly. The reason is that state variables become correlated after a few steps. The main innovation in this paper is a method for sidestepping this problem by redefining state variables dynamically at each time step such that the posterior for time t is represented in a factored form. This update is done using a progression algorithm as a subroutine, and our algorithm’s tractability follows when that subroutine is tractable. Our results are for general deterministic actions and in particular, our algorithm is tractable for one-to-one and STRIPS actions. We apply our reasoning algorithm about deterministic actions to reasoning about sequences of probabilistic actions and improve the efficiency of the current probabilistic reasoning approaches. We demonstrate the efficiency of the new algorithm empirically over AI-Planning data sets.