# Efficient Shield Synthesis via State-Space Transformation

arXiv: https://arxiv.org/abs/2407.19911 · HTML: https://mlsanity.com/paper/2407.19911/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 29 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [A predictive safety filter for learning-based control of constrained nonlinear dynamical systems](https://mlsanity.com/paper/1812.05506/) (2018)
- [Shield Synthesis: Runtime Enforcement for Reactive Systems](https://mlsanity.com/paper/1501.02573/) (2015)
- [Shielded Reinforcement Learning for Hybrid Systems](https://mlsanity.com/paper/2308.14424/) (2023)
- [Optimized State Space Grids for Abstractions](https://mlsanity.com/paper/1711.01637/) (2017)
- [Efficient Local Computation of Differential Bisimulations via Coupling and Up-to Methods](https://mlsanity.com/paper/2104.13160/) (2021)
- [Lazy Abstraction-Based Control for Safety Specifications](https://mlsanity.com/paper/1804.02666/) (2018)
- [State-feedback Abstractions for Optimal Control of Piecewise-affine Systems](https://mlsanity.com/paper/2204.00315/) (2022)
- [Dionysos.jl: a Modular Platform for Smart Symbolic Control](https://mlsanity.com/paper/2404.14114/) (2024)

## Built on by (most cited first, 4 of 4)

- [Compositional Shielding and Reinforcement Learning for Multi-Agent Systems](https://mlsanity.com/paper/2410.10460/) (2024)
- [Robust Probabilistic Shielding for Safe Offline Reinforcement Learning](https://mlsanity.com/paper/2605.10293/) (2026)
- [Uppaal Coshy: Automatic Synthesis of Compact Shields for Hybrid Systems](https://mlsanity.com/paper/2508.16345/) (2025)
- [Efficient Dynamic Shielding for Parametric Safety Specifications](https://mlsanity.com/paper/2505.22104/) (2025)

## Abstract (arXiv)

We consider the problem of synthesizing safety strategies for control systems, also known as shields. Since the state space is infinite, shields are typically computed over a finite-state abstraction, with the most common abstraction being a rectangular grid. However, for many systems, such a grid does not align well with the safety property or the system dynamics. That is why a coarse grid is rarely sufficient, but a fine grid is typically computationally infeasible to obtain. In this paper, we show that appropriate state-space transformations can still allow to use a coarse grid at almost no computational overhead. We demonstrate in three case studies that our transformation-based synthesis outperforms a standard synthesis by several orders of magnitude. In the first two case studies, we use domain knowledge to select a suitable transformation. In the third case study, we instead report on results in engineering a transformation without domain knowledge.