# Safe Exploration in Continuous Action Spaces

arXiv: https://arxiv.org/abs/1801.08757 · HTML: https://mlsanity.com/paper/1801.08757/

## Key facts

- Cited by 247 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2018.

## Built on by (most cited first, 30 of 247)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Do the Rewards Justify the Means? Measuring Trade-Offs Between Rewards and Ethical Behavior in the MACHIAVELLI Benchmark](https://mlsanity.com/paper/2304.03279/) (2023)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [Constraints Penalized Q-learning for Safe Offline Reinforcement Learning](https://mlsanity.com/paper/2107.09003/) (2021)
- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [SafeVLA: Towards Safety Alignment of Vision-Language-Action Model via Constrained Learning](https://mlsanity.com/paper/2503.03480/) (2025)
- [Constrained Variational Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/2201.11927/) (2022)
- [Saute RL: Almost Surely Safe Reinforcement Learning Using State Augmentation](https://mlsanity.com/paper/2202.06558/) (2022)
- [Constrained Decision Transformer for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2302.07351/) (2023)
- [f-IRL: Inverse Reinforcement Learning via State Marginal Matching](https://mlsanity.com/paper/2011.04709/) (2020)
- [Safe Reinforcement Learning by Imagining the Near Future](https://mlsanity.com/paper/2202.07789/) (2022)
- [Safe Offline Reinforcement Learning with Feasibility-Guided Diffusion Model](https://mlsanity.com/paper/2401.10700/) (2024)
- [Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments](https://mlsanity.com/paper/2209.15090/) (2022)
- [Datasets and Benchmarks for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2306.09303/) (2023)
- [Exploration in Deep Reinforcement Learning: From Single-Agent to Multiagent Domain](https://mlsanity.com/paper/2109.06668/) (2021)
- [Constrained Update Projection Approach to Safe Policy Optimization](https://mlsanity.com/paper/2209.07089/) (2022)
- [Constrained Policy Optimization via Bayesian World Models](https://mlsanity.com/paper/2201.09802/) (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)
- [Correlated Proxies: A New Definition and Improved Mitigation for Reward Hacking](https://mlsanity.com/paper/2403.03185/) (2024)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Safe Reinforcement Learning Using Advantage-Based Intervention](https://mlsanity.com/paper/2106.09110/) (2021)
- [A Survey of Constraint Formulations in Safe Reinforcement Learning](https://mlsanity.com/paper/2402.02025/) (2024)
- [Safe Reinforcement Learning via Probabilistic Logic Shields](https://mlsanity.com/paper/2303.03226/) (2023)
- [Learning Barrier Certificates: Towards Safe Reinforcement Learning with Zero Training-time Violations](https://mlsanity.com/paper/2108.01846/) (2021)
- [On the Robustness of Safe Reinforcement Learning under Observational Perturbations](https://mlsanity.com/paper/2205.14691/) (2022)
- [Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizability](https://mlsanity.com/paper/2209.08025/) (2022)
- [Safe Reinforcement Learning for Legged Locomotion](https://mlsanity.com/paper/2203.02638/) (2022)
- [Provably Safe Reinforcement Learning: Conceptual Analysis, Survey, and Benchmarking](https://mlsanity.com/paper/2205.06750/) (2022)
- [Context-Aware Safe Reinforcement Learning for Non-Stationary Environments](https://mlsanity.com/paper/2101.00531/) (2021)

## Abstract (arXiv)

We address the problem of deploying a reinforcement learning (RL) agent on a physical system such as a datacenter cooling unit or robot, where critical constraints must never be violated. We show how to exploit the typically smooth dynamics of these systems and enable RL algorithms to never violate constraints during learning. Our technique is to directly add to the policy a safety layer that analytically solves an action correction formulation per each state. The novelty of obtaining an elegant closed-form solution is attained due to a linearized model, learned on past trajectories consisting of arbitrary actions. This is to mimic the real-world circumstances where data logs were generated with a behavior policy that is implausible to describe mathematically; such cases render the known safety-aware off-policy methods inapplicable. We demonstrate the efficacy of our approach on new representative physics-based environments, and prevail where reward shaping fails by maintaining zero constraint violations.