Planning in Discrete and Continuous Markov Decision Processes by Probabilistic Programming

Real-world planning problems frequently involve mixtures of continuous and discrete state variables and actions, and are formulated in environments with an unknown number of objects. In recent years, probabilistic programming has emerged as a natural approach to capture and characterize such complex probability distributions with general-purpose inference methods. While it is known that a probabilistic programming language can be easily extended to represent Markov Decision Processes (MDPs) for planning tasks, solving such tasks is challenging. Building on related efforts in reinforcement learning, we introduce a conceptually simple but powerful planning algorithm for MDPs realized as a probabilistic program. This planner constructs approximations to the optimal policy by importance sampling, while exploiting the knowledge of the MDP model. In our empirical evaluations, we show that this approach has wide applicability on domains ranging from strictly discrete to strictly continuous to hybrid ones, handles intricacies such as unknown objects, and is argued to be competitive given its generality.