Data-Driven Invariant Learning for Probabilistic Programs
30/09/2022
Speaker
Abstract
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, and also works with black-box access to the program. 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.
Joint work with Jialu Bao, Nitesh Trivedi, Drashti Pathak, and Subhajit Roy.
Bio
Justin Hsu is an assistant professor of Computer Science at Cornell University. He was previously an assistant professor at UW-Madison and a postdoc at Cornell and UCL, after receiving his doctorate in Computer Science from the University of Pennsylvania. His research focuses on formal verification of probabilistic programs, including algorithms from differential privacy, protocols from cryptography, and mechanisms from game theory. His work has been recognized by an NSF CAREER award, a SIGPLAN John C. Reynolds Doctoral Dissertation award, distinguished paper awards from POPL and CAV, and industrial awards from Facebook.