# Deep Reinforcement Learning for Reach-Avoid-Stay Problems

arXiv: https://arxiv.org/abs/2410.02898 · HTML: https://mlsanity.com/paper/2410.02898/

## Key facts

- Cited by 1 papers in the map (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 27 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## 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)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learning](https://mlsanity.com/paper/2112.12288/) (2021)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [ISAACS: Iterative Soft Adversarial Actor-Critic for Safety](https://mlsanity.com/paper/2212.03228/) (2022)
- [Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees](https://mlsanity.com/paper/2201.08355/) (2022)
- [Robot Learning of Mobile Manipulation with Reachability Behavior Priors](https://mlsanity.com/paper/2203.04051/) (2022)
- [A Hamilton-Jacobi Reachability-Based Framework for Predicting and Analyzing Human Motion for Safe Planning](https://mlsanity.com/paper/1910.13369/) (2019)
- [Infinite-Horizon Reach-Avoid Zero-Sum Games via Deep Reinforcement Learning](https://mlsanity.com/paper/2203.10142/) (2022)
- [Certifiable Reachability Learning Using a New Lipschitz Continuous Value Function](https://mlsanity.com/paper/2408.07866/) (2024)
- [Funnel-based Control for Reach-Avoid-Stay Specifications](https://mlsanity.com/paper/2308.15803/) (2023)

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

- [Back to Base: Towards Hands-Off Learning via Safe Resets with Reach-Avoid Safety Filters](https://mlsanity.com/paper/2501.02620/) (2025)

## Abstract (arXiv)

Reach-Avoid-Stay (RAS) tasks are essential in applications where systems must safely reach a target set and remain within it under all bounded disturbances. Existing approaches either struggle to compute the maximal robust RAS set, the set of all states from which the RAS task is achievable, or are limited in handling general dynamic systems. To address these challenges, this paper proposes a two-step deep reinforcement learning framework that jointly learns the maximal robust RAS set and the corresponding control policy. The first step identifies the maximal robust control-invariant set within the target set and derives a policy that ensures the system remains within it. The second step computes the maximal robust reach-avoid (RA) set using this invariant set as the target, and it is proven that this RA set is equivalent to the maximal robust RAS set. Leveraging this result, a switching policy is constructed from the two step-wise policies, which constitutes a valid policy guaranteeing completion of the RAS task. Simulation results demonstrate that the proposed framework (1) computes the exact maximal robust RAS set in the absence of training errors, yielding the least restrictive RAS policy, and (2) identifies the RAS set with high accuracy while outperforming baseline methods on RAS tasks.