# Safety Guarantees in Zero-Shot Reinforcement Learning for Cascade Dynamical Systems

arXiv: https://arxiv.org/abs/2604.10429 · HTML: https://mlsanity.com/paper/2604.10429/

## 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 14 of its 26 references that are in the map.
- First posted on arXiv 12 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, 14 of 14)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Sim-to-Real Transfer in Deep Reinforcement Learning for Robotics: a Survey](https://mlsanity.com/paper/2009.13303/) (2020)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [A predictive safety filter for learning-based control of constrained nonlinear dynamical systems](https://mlsanity.com/paper/1812.05506/) (2018)
- [Safe Policies for Reinforcement Learning via Primal-Dual Methods](https://mlsanity.com/paper/1911.09101/) (2019)
- [Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees](https://mlsanity.com/paper/2201.08355/) (2022)
- [Probabilistic Constraint for Safety-Critical Reinforcement Learning](https://mlsanity.com/paper/2306.17279/) (2023)
- [SPiDR: A Simple Approach for Zero-Shot Safety in Sim-to-Real Transfer](https://mlsanity.com/paper/2509.18648/) (2025)
- [Reinforcement Learning for Reduced-order Models of Legged Robots](https://mlsanity.com/paper/2310.09873/) (2023)
- [Safety-Critical Control with Bounded Inputs via Reduced Order Models](https://mlsanity.com/paper/2303.03247/) (2023)
- [Transfer Learning for a Class of Cascade Dynamical Systems](https://mlsanity.com/paper/2410.06828/) (2024)

## Abstract (arXiv)

This paper considers the problem of zero-shot safety guarantees for cascade dynamical systems. These are systems where a subset of the states (the inner states) affects the dynamics of the remaining states (the outer states) but not vice-versa. We define safety as remaining on a set deemed safe for all times with high probability. We propose to train a safe RL policy on a reduced-order model, which ignores the dynamics of the inner states, but it treats it as an action that influences the outer state. Thus, reducing the complexity of the training. When deployed in the full system the trained policy is combined with a low-level controller whose task is to track the reference provided by the RL policy. Our main theoretical contribution is a bound on the safe probability in the full-order system. In particular, we establish the interplay between the probability of remaining safe after the zero-shot deployment and the quality of the tracking of the inner states. We validate our theoretical findings on a quadrotor navigation task, demonstrating that the preservation of the safety guarantees is tied to the bandwidth and tracking capabilities of the low-level controller.