Data-Driven Invariant Learning for Probabilistic Programs

Morgan and McIver's weakest pre-expectation framework is one of the most well-established methods for deductive verification of probabilistic programs. Roughly, the idea is to generalize binary state assertions to real-valued expectations, which can measure expected values of probabilistic program quantities. While loop-free programs can be analyzed by mechanically transforming expectations, verifying loops usually requires finding an invariant expectation, a difficult task. We propose a new view of invariant expectation synthesis as a regression problem: given an input state, predict the average value of the post-expectation in the output distribution. Guided by this perspective, we develop the first data-driven invariant synthesis method for probabilistic programs. Unlike prior work on probabilistic invariant inference, our approach can learn piecewise continuous invariants without relying on template expectations. We also develop a data-driven approach to learn sub-invariants from data, which can be used to upper- or lower-bound expected values. We implement our approaches and demonstrate their effectiveness on a variety of benchmarks from the probabilistic programming literature.