# Learning-Based Synthesis of Safety Controllers

## TL;DR

This paper introduces a machine learning framework for synthesizing reactive safety controllers in complex systems modeled by infinite-duration games, leveraging a novel decision tree learning algorithm to efficiently approximate winning regions.

## Contribution

It presents a new decision tree learning approach for safety controller synthesis in infinite and large finite graphs, with convergence guarantees and empirical performance evaluation.

## Key findings

- The decision tree algorithm guarantees convergence to a safety controller.
- The framework effectively handles infinite and large finite graphs.
- Empirical results show competitive performance against existing methods.

## Abstract

We propose a machine learning framework to synthesize reactive controllers for systems whose interactions with their adversarial environment are modeled by infinite-duration, two-player games over (potentially) infinite graphs. Our framework targets safety games with infinitely many vertices, but it is also applicable to safety games over finite graphs whose size is too prohibitive for conventional synthesis techniques. The learning takes place in a feedback loop between a teacher component, which can reason symbolically about the safety game, and a learning algorithm, which successively learns an overapproximation of the winning region from various kinds of examples provided by the teacher. We develop a novel decision tree learning algorithm for this setting and show that our algorithm is guaranteed to converge to a reactive safety controller if a suitable overapproximation of the winning region can be expressed as a decision tree. Finally, we empirically compare the performance of a prototype implementation to existing approaches, which are based on constraint solving and automata learning, respectively.