# Learning over Forward-Invariant Policy Classes: Reinforcement Learning without Safety Concerns

arXiv: https://arxiv.org/abs/2604.07875 · HTML: https://mlsanity.com/paper/2604.07875/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 8 of 8)

- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Reinforcement Learning for UAV Attitude Control](https://mlsanity.com/paper/1804.04154/) (2018)
- [Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes](https://mlsanity.com/paper/1603.04915/) (2016)
- [Differential Flatness of Quadrotor Dynamics Subject to Rotor Drag for Accurate Tracking of High-Speed Trajectories](https://mlsanity.com/paper/1712.02402/) (2017)

## Abstract (arXiv)

This paper proposes a safe reinforcement learning (RL) framework based on forward-invariance-induced action-space design. The control problem is cast as a Markov decision process, but instead of relying on runtime shielding or penalty-based constraints, safety is embedded directly into the action representation. Specifically, we construct a finite admissible action set in which each discrete action corresponds to a stabilizing feedback law that preserves forward invariance of a prescribed safe state set. Consequently, the RL agent optimizes policies over a safe-by-construction policy class. We validate the framework on a quadcopter hover-regulation problem under disturbance. Simulation results show that the learned policy improves closed-loop performance and switching efficiency, while all evaluated policies remain safety-preserving. The proposed formulation decouples safety assurance from performance optimization and provides a promising foundation for safe learning in nonlinear systems.