Bounded Expectations: Resource Analysis for Probabilistic Programs

TL;DR

This paper introduces a fully automatic static analysis technique for deriving upper bounds on the expected resource consumption of probabilistic programs, combining manual reasoning methods with automatic analysis.

Contribution

It extends automatic amortized resource analysis to probabilistic programs and automates manual reasoning using weakest preconditions, enabling efficient bound inference.

Findings

Successfully analyzed 39 probabilistic programs and randomized algorithms.

Derived bounds are very precise and often optimal.

Bound inference reduces to LP solving in many cases.

Abstract

This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs. The new technique combines manual state-of-the-art reasoning techniques for probabilistic programs with an effective method for automatic resource-bound analysis of deterministic programs. It can be seen as both, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning for probabilistic programs that is based on weakest preconditions. As a result, bound inference can be reduced to off-the-shelf LP solving in many cases and automatically-derived bounds can be interactively extended with standard program logics if the automation fails. Building on existing work, the soundness of the analysis is proved with respect to an operational semantics that is based on Markov decision processes. The effectiveness of the technique is demonstrated with a prototype implementation that is used to automatically analyze 39 challenging probabilistic programs and randomized algorithms. Experimental results indicate that the derived constant factors in the bounds are very precise and even optimal for many programs.