noDice: Inference for Discrete Probabilistic Programs with Nondeterminism and Conditioning

Abstract

Probabilistic programming languages (PPLs) are an expressive and intuitive means of representing complex probability distributions. In that realm, languages like Dice target an important class of probabilistic programs: those whose probability distributions are discrete. Discrete distributions are common in many fields, including text analysis, network verification, artificial intelligence, and graph analysis. Another important feature in the world of probabilistic modeling are nondeterministic choices as found in Markov Decision Processes (MDPs) which play a major role in reinforcement learning. Modern PPLs usually lack support for nondeterminism. We address this gap with the introduction of noDice, which extends the discrete probabilistic inference engine Dice. noDice performs inference on loop-free programs by constructing an MDP so that the distributions modeled by the program correspond to schedulers in the MDP. Furthermore, decision diagrams are used as an intermediate step to exploit the program structure and drastically reduce the state space of the MDP.