# Barrier Certified Safety Learning Control: When Sum-of-Square Programming Meets Reinforcement Learning

arXiv: https://arxiv.org/abs/2206.07915 · HTML: https://mlsanity.com/paper/2206.07915/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 16 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Benchmarking Deep Reinforcement Learning for Continuous Control](https://mlsanity.com/paper/1604.06778/) (2016)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots](https://mlsanity.com/paper/2103.14295/) (2021)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Control Regularization for Reduced Variance Reinforcement Learning](https://mlsanity.com/paper/1905.05380/) (2019)
- [Safe Learning of Quadrotor Dynamics Using Barrier Certificates](https://mlsanity.com/paper/1710.05472/) (2017)
- [Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squares](https://mlsanity.com/paper/1802.08917/) (2018)
- [Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions](https://mlsanity.com/paper/2109.12313/) (2021)
- [SOSOPT: A Toolbox for Polynomial Optimization](https://mlsanity.com/paper/1308.1889/) (2013)
- [On Estimating the Probabilistic Region of Attraction for Partially Unknown Nonlinear Systems: An Sum-of-Squares Approach](https://mlsanity.com/paper/2110.08781/) (2021)
- [Sum-of-Squares Program and Safe Learning On Maximizing the Region of Attraction of Partially Unknown Systems](https://mlsanity.com/paper/2201.00137/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Review On Safe Reinforcement Learning Using Lyapunov and Barrier Functions](https://mlsanity.com/paper/2508.09128/) (2025)

## Abstract (arXiv)

Safety guarantee is essential in many engineering implementations. Reinforcement learning provides a useful way to strengthen safety. However, reinforcement learning algorithms cannot completely guarantee safety over realistic operations. To address this issue, this work adopts control barrier functions over reinforcement learning, and proposes a compensated algorithm to completely maintain safety. Specifically, a sum-of-squares programming has been exploited to search for the optimal controller, and tune the learning hyperparameters simultaneously. Thus, the control actions are pledged to be always within the safe region. The effectiveness of proposed method is demonstrated via an inverted pendulum model. Compared to quadratic programming based reinforcement learning methods, our sum-of-squares programming based reinforcement learning has shown its superiority.