# Shields to Guarantee Probabilistic Safety in MDPs

arXiv: https://arxiv.org/abs/2605.10888 · HTML: https://mlsanity.com/paper/2605.10888/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 28 of 28)

- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [The Probabilistic Model Checker Storm](https://mlsanity.com/paper/2002.07080/) (2020)
- [Safe Multi-Agent Reinforcement Learning via Shielding](https://mlsanity.com/paper/2101.11196/) (2021)
- [Safe Reinforcement Learning via Shielding under Partial Observability](https://mlsanity.com/paper/2204.00755/) (2022)
- [Cautious Reinforcement Learning with Logical Constraints](https://mlsanity.com/paper/2002.12156/) (2020)
- [Safe Reinforcement Learning via Probabilistic Logic Shields](https://mlsanity.com/paper/2303.03226/) (2023)
- [Provably Safe Reinforcement Learning: Conceptual Analysis, Survey, and Benchmarking](https://mlsanity.com/paper/2205.06750/) (2022)
- [Safety-Constrained Reinforcement Learning for MDPs](https://mlsanity.com/paper/1510.05880/) (2015)
- [Neural Simplex Architecture](https://mlsanity.com/paper/1908.00528/) (2019)
- [Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes](https://mlsanity.com/paper/2210.10691/) (2022)
- [Online Shielding for Reinforcement Learning](https://mlsanity.com/paper/2212.01861/) (2022)
- [Adaptive Shielding under Uncertainty](https://mlsanity.com/paper/2010.03842/) (2020)
- [Permissive Controller Synthesis for Probabilistic Systems](https://mlsanity.com/paper/1504.04662/) (2015)
- [Shield Synthesis for LTL Modulo Theories](https://mlsanity.com/paper/2406.04184/) (2024)
- [Probabilistic Shielding for Safe Reinforcement Learning](https://mlsanity.com/paper/2503.07671/) (2025)
- [Dynamic Shielding for Reinforcement Learning in Black-Box Environments](https://mlsanity.com/paper/2207.13446/) (2022)
- [Automata Learning meets Shielding](https://mlsanity.com/paper/2212.01838/) (2022)
- [Safe POMDP Online Planning via Shielding](https://mlsanity.com/paper/2309.10216/) (2023)
- [Compositional Shielding and Reinforcement Learning for Multi-Agent Systems](https://mlsanity.com/paper/2410.10460/) (2024)
- [Optimizing Expectation with Guarantees in POMDPs (Technical Report)](https://mlsanity.com/paper/1611.08696/) (2016)
- [Safe Reinforcement Learning in Black-Box Environments via Adaptive Shielding](https://mlsanity.com/paper/2405.18180/) (2024)
- [Reinforcement Learning of Risk-Constrained Policies in Markov Decision Processes](https://mlsanity.com/paper/2002.12086/) (2020)
- [Adaptive Shielding via Parametric Safety Proofs](https://mlsanity.com/paper/2502.18879/) (2025)
- [On Optimizing the Conditional Value-at-Risk of a Maximum Cost for Risk-Averse Safety Analysis](https://mlsanity.com/paper/2106.00776/) (2021)
- [The Use of the Simplex Architecture to Enhance Safety in Deep-Learning-Powered Autonomous Systems](https://mlsanity.com/paper/2509.21014/) (2025)
- [Formally-Sharp DAgger for MCTS: Lower-Latency Monte Carlo Tree Search using Data Aggregation with Formal Methods](https://mlsanity.com/paper/2308.07738/) (2023)
- [Finite-State Controllers for (Hidden-Model) POMDPs using Deep Reinforcement Learning](https://mlsanity.com/paper/2602.08734/) (2026)

## Built on by (most cited first, 2 of 2)

- [Cycle-Consistent Neural Explanation of Formal Verification Certificates](https://mlsanity.com/paper/2606.24414/) (2026)
- [Adaptive Probabilistic Shielding by Learning MDPs for Safe Reinforcement Learning](https://mlsanity.com/paper/2608.19836/) (2026)

## Abstract (arXiv)

Shielding is a prominent model-based technique to ensure safety of autonomous agents. Classical shielding aims to ensure that nothing bad ever happens and comes with strong guarantees about safety and maximal permissiveness. However, shielding systems for probabilistic safety, where something bad is allowed to happen with an acceptable probability, has proven to be more intricate. This paper presents a formal framework that conservatively extends classical shields to probabilistic safety. In this framework, we (i) demonstrate the impossibility of preserving the strong guarantees on safety and permissiveness, (ii) provide natural shields with weaker guarantees, and (iii) introduce offline and online shield constructions ensuring strong safety guarantees. The empirical evaluation highlights the practical advantages of the new shields, as well as their computational feasibility.