# Lyapunov-based uncertainty-aware safe reinforcement learning

arXiv: https://arxiv.org/abs/2107.13944 · HTML: https://mlsanity.com/paper/2107.13944/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 29 Jul 2021.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulation](https://mlsanity.com/paper/1806.10293/) (2018)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Emergent Complexity and Zero-shot Transfer via Unsupervised Environment Design](https://mlsanity.com/paper/2012.02096/) (2020)
- [CAD2RL: Real Single-Image Flight without a Single Real Image](https://mlsanity.com/paper/1611.04201/) (2016)
- [Adaptive Attention Span in Transformers](https://mlsanity.com/paper/1905.07799/) (2019)
- [Lyapunov-based Safe Policy Optimization for Continuous Control](https://mlsanity.com/paper/1901.10031/) (2019)
- [Augmenting Self-attention with Persistent Memory](https://mlsanity.com/paper/1907.01470/) (2019)
- [Uncertainty-Aware Reinforcement Learning for Collision Avoidance](https://mlsanity.com/paper/1702.01182/) (2017)
- [Safe Reinforcement Learning with Model Uncertainty Estimates](https://mlsanity.com/paper/1810.08700/) (2018)
- [Making Efficient Use of Demonstrations to Solve Hard Exploration Problems](https://mlsanity.com/paper/1909.01387/) (2019)
- [Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes](https://mlsanity.com/paper/1603.04915/) (2016)
- [Adaptive Transformers in RL](https://mlsanity.com/paper/2004.03761/) (2020)

## Built on by (most cited first, 3 of 3)

- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [A Review On Safe Reinforcement Learning Using Lyapunov and Barrier Functions](https://mlsanity.com/paper/2508.09128/) (2025)
- [Safe Reinforcement Learning for Power System Control: A Review](https://mlsanity.com/paper/2407.00681/) (2024)

## Abstract (arXiv)

Reinforcement learning (RL) has shown a promising performance in learning optimal policies for a variety of sequential decision-making tasks. However, in many real-world RL problems, besides optimizing the main objectives, the agent is expected to satisfy a certain level of safety (e.g., avoiding collisions in autonomous driving). While RL problems are commonly formalized as Markov decision processes (MDPs), safety constraints are incorporated via constrained Markov decision processes (CMDPs). Although recent advances in safe RL have enabled learning safe policies in CMDPs, these safety requirements should be satisfied during both training and in the deployment process. Furthermore, it is shown that in memory-based and partially observable environments, these methods fail to maintain safety over unseen out-of-distribution observations. To address these limitations, we propose a Lyapunov-based uncertainty-aware safe RL model. The introduced model adopts a Lyapunov function that converts trajectory-based constraints to a set of local linear constraints. Furthermore, to ensure the safety of the agent in highly uncertain environments, an uncertainty quantification method is developed that enables identifying risk-averse actions through estimating the probability of constraint violations. Moreover, a Transformers model is integrated to provide the agent with memory to process long time horizons of information via the self-attention mechanism. The proposed model is evaluated in grid-world navigation tasks where safety is defined as avoiding static and dynamic obstacles in fully and partially observable environments. The results of these experiments show a significant improvement in the performance of the agent both in achieving optimality and satisfying safety constraints.