Data-Driven Invariant Learning for Probabilistic Programs

TL;DR

This paper introduces a novel data-driven method for synthesizing invariants in probabilistic programs, enabling automatic inference of piecewise continuous invariants and sub-invariants without templates, even with black-box access.

Contribution

It presents the first data-driven invariant synthesis technique for probabilistic programs, capable of learning complex invariants and sub-invariants directly from data.

Findings

Successfully synthesized invariants on multiple benchmarks

Outperformed existing methods in invariant accuracy

Demonstrated effectiveness with black-box program access

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.