Inductive Synthesis for Probabilistic Programs Reaches New Horizons

TL;DR

This paper introduces a new inductive synthesis method for probabilistic programs that efficiently prunes candidate programs using counter-examples, significantly accelerating the synthesis process, especially for complex problems.

Contribution

It presents a novel inductive oracle for counter-example generation and a hybrid approach that combines inductive and deductive reasoning to improve probabilistic program synthesis.

Findings

Faster synthesis times on benchmark problems

Reduced runtime from days to minutes for complex tasks

Effective pruning strategy with counter-examples

Abstract

This paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a PCTL specification. The method builds on a novel inductive oracle that greedily generates counter-examples (CEs) for violating programs and uses them to prune the family. These CEs leverage the semantics of the family in the form of bounds on its best- and worst-case behaviour provided by a deductive oracle using an MDP abstraction. The method further monitors the performance of the synthesis and adaptively switches between the inductive and deductive reasoning. Our experiments demonstrate that the novel CE construction provides a significantly faster and more effective pruning strategy leading to acceleration of the synthesis process on a wide range of benchmarks. For challenging problems, such as the synthesis of decentralized partially-observable controllers, we reduce the run-time from a day to minutes.