# Robust Safe Reinforcement Learning under Adversarial Disturbances

arXiv: https://arxiv.org/abs/2310.07207 · HTML: https://mlsanity.com/paper/2310.07207/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 18 of 18)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Sim-to-Real Transfer in Deep Reinforcement Learning for Robotics: a Survey](https://mlsanity.com/paper/2009.13303/) (2020)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [A Review of Robot Learning for Manipulation: Challenges, Representations, and Algorithms](https://mlsanity.com/paper/1907.03146/) (2019)
- [Learning to Walk in the Real World with Minimal Human Effort](https://mlsanity.com/paper/2002.08550/) (2020)
- [Reachability Constrained Reinforcement Learning](https://mlsanity.com/paper/2205.07536/) (2022)
- [State-wise Safe Reinforcement Learning: A Survey](https://mlsanity.com/paper/2302.03122/) (2023)
- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [Integrated Decision and Control: Towards Interpretable and Computationally Efficient Driving Intelligence](https://mlsanity.com/paper/2103.10290/) (2021)
- [Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning](https://mlsanity.com/paper/2111.07695/) (2021)

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

- [Learning Predictive Safety Filter via Decomposition of Robust Invariant Set](https://mlsanity.com/paper/2311.06769/) (2023)
- [TCRL: Temporal-Coupled Adversarial Training for Robust Constrained Reinforcement Learning in Worst-Case Scenarios](https://mlsanity.com/paper/2602.13040/) (2026)
- [FlexServe: A Fast and Secure LLM Serving System for Mobile Devices with Flexible Resource Isolation](https://mlsanity.com/paper/2603.09046/) (2026)
- [FlexServe: A Fast and Secure LLM Serving System for Mobile Devices with Flexible Resource Isolation](https://mlsanity.com/paper/2606.23370/) (2026)

## Abstract (arXiv)

Safety is a primary concern when applying reinforcement learning to real-world control tasks, especially in the presence of external disturbances. However, existing safe reinforcement learning algorithms rarely account for external disturbances, limiting their applicability and robustness in practice. To address this challenge, this paper proposes a robust safe reinforcement learning framework that tackles worst-case disturbances. First, this paper presents a policy iteration scheme to solve for the robust invariant set, i.e., a subset of the safe set, where persistent safety is only possible for states within. The key idea is to establish a two-player zero-sum game by leveraging the safety value function in Hamilton-Jacobi reachability analysis, in which the protagonist (i.e., control inputs) aims to maintain safety and the adversary (i.e., external disturbances) tries to break down safety. This paper proves that the proposed policy iteration algorithm converges monotonically to the maximal robust invariant set. Second, this paper integrates the proposed policy iteration scheme into a constrained reinforcement learning algorithm that simultaneously synthesizes the robust invariant set and uses it for constrained policy optimization. This algorithm tackles both optimality and safety, i.e., learning a policy that attains high rewards while maintaining safety under worst-case disturbances. Experiments on classic control tasks show that the proposed method achieves zero constraint violation with learned worst-case adversarial disturbances, while other baseline algorithms violate the safety constraints substantially. Our proposed method also attains comparable performance as the baselines even in the absence of the adversary.