# CSPO: Constraint-Sensitive Policy Optimization for Safe Reinforcement Learning

arXiv: https://arxiv.org/abs/2606.14415 · HTML: https://mlsanity.com/paper/2606.14415/

## 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 19 of its 27 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [Safety-Gymnasium: A Unified Safe Reinforcement Learning Benchmark](https://mlsanity.com/paper/2310.12567/) (2023)
- [IPO: Interior-point Policy Optimization under Constraints](https://mlsanity.com/paper/1910.09615/) (2019)
- [OmniSafe: An Infrastructure for Accelerating Safe Reinforcement Learning Research](https://mlsanity.com/paper/2305.09304/) (2023)
- [Penalized Proximal Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/2205.11814/) (2022)
- [Constrained Update Projection Approach to Safe Policy Optimization](https://mlsanity.com/paper/2209.07089/) (2022)
- [Evaluating Model-free Reinforcement Learning toward Safety-critical Tasks](https://mlsanity.com/paper/2212.05727/) (2022)
- [Embedding Safety into RL: A New Take on Trust Region Methods](https://mlsanity.com/paper/2411.02957/) (2024)
- [Exterior Penalty Policy Optimization with Penalty Metric Network under Constraints](https://mlsanity.com/paper/2407.15537/) (2024)
- [Adaptive Primal-Dual Method for Safe Reinforcement Learning](https://mlsanity.com/paper/2402.00355/) (2024)

## Abstract (arXiv)

Safe reinforcement learning (Safe RL) aims to maximize expected return while satisfying safety constraints, typically modeled as Constrained Markov Decision Processes (CMDPs). While primal-dual methods scale well to deep RL, they often suffer from delayed constraint correction, leading to oscillatory behavior and prolonged safety violations. In this paper, we propose Constraint-Sensitive Policy Optimization (CSPO), a first-order primal-dual method that incorporates local constraint sensitivity into policy updates. CSPO augments the primal objective with a constraint-sensitive correction derived from the shortest signed distance to the safety boundary, enabling smarter recovery steps back to safety, compensating for delayed Lagrange multiplier updates, reducing oscillations near the boundary, and preserving the KKT solutions of the original constrained problem. Experiments on navigation and locomotion benchmarks demonstrate that CSPO achieves faster safety recovery and high reward preservation, resulting in higher constrained returns compared to state-of-the-art primal-dual and penalty-based methods