# A Learnable Safety Measure

arXiv: https://arxiv.org/abs/1910.02835 · HTML: https://mlsanity.com/paper/1910.02835/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2019.

## Built on by (most cited first, 7 of 7)

- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [Safe Value Functions](https://mlsanity.com/paper/2105.12204/) (2021)
- [Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processes](https://mlsanity.com/paper/2405.10581/) (2024)
- [Viability of Future Actions: Robust Safety in Reinforcement Learning via Entropy Regularization](https://mlsanity.com/paper/2506.10871/) (2025)
- [Ergodicity in reinforcement learning](https://mlsanity.com/paper/2603.10895/) (2026)
- [Attainment Regions in Feature-Parameter Space for High-Level Debugging in Autonomous Robots](https://mlsanity.com/paper/2108.03150/) (2021)

## Abstract (arXiv)

Failures are challenging for learning to control physical systems since they risk damage, time-consuming resets, and often provide little gradient information. Adding safety constraints to exploration typically requires a lot of prior knowledge and domain expertise. We present a safety measure which implicitly captures how the system dynamics relate to a set of failure states. Not only can this measure be used as a safety function, but also to directly compute the set of safe state-action pairs. Further, we show a model-free approach to learn this measure by active sampling using Gaussian processes. While safety can only be guaranteed after learning the safety measure, we show that failures can already be greatly reduced by using the estimated measure during learning.