# Myopically Verifiable Probabilistic Certificates for Safe Control and Learning

arXiv: https://arxiv.org/abs/2404.16883 · HTML: https://mlsanity.com/paper/2404.16883/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 83 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 30 of 41)

- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guarantee](https://mlsanity.com/paper/2011.05869/) (2020)
- [Learning to be Safe: Deep RL with a Safety Critic](https://mlsanity.com/paper/2010.14603/) (2020)
- [Safe Reinforcement Learning in Constrained Markov Decision Processes](https://mlsanity.com/paper/2008.06626/) (2020)
- [Safe Reinforcement Learning Using Robust Control Barrier Functions](https://mlsanity.com/paper/2110.05415/) (2021)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [Robust Model Predictive Shielding for Safe Reinforcement Learning with Stochastic Dynamics](https://mlsanity.com/paper/1910.10885/) (2019)
- [A Primal-Dual Approach to Constrained Markov Decision Processes](https://mlsanity.com/paper/2101.10895/) (2021)
- [Enforcing robust control guarantees within neural network policies](https://mlsanity.com/paper/2011.08105/) (2020)
- [Safe Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2106.06239/) (2021)
- [Learning Control Policies for Stochastic Systems with Reach-avoid Guarantees](https://mlsanity.com/paper/2210.05308/) (2022)
- [Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs](https://mlsanity.com/paper/2009.01196/) (2020)
- [Safe Control with Neural Network Dynamic Models](https://mlsanity.com/paper/2110.01110/) (2021)
- [Decentralized Control of Quadrotor Swarms with End-to-end Deep Reinforcement Learning](https://mlsanity.com/paper/2109.07735/) (2021)
- [Learning Safe Neural Network Controllers with Barrier Certificates](https://mlsanity.com/paper/2009.09826/) (2020)
- [A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems](https://mlsanity.com/paper/1902.11277/) (2019)
- [A Barrier Function Approach to Finite-Time Stochastic System Verification and Control](https://mlsanity.com/paper/1909.05109/) (2019)
- [Control Barrier Functions for Stochastic Systems](https://mlsanity.com/paper/2003.03498/) (2020)
- [Safety Guarantees for Neural Network Dynamic Systems via Stochastic Barrier Functions](https://mlsanity.com/paper/2206.07811/) (2022)
- [Learning Risk-Aware Quadrupedal Locomotion using Distributional Reinforcement Learning](https://mlsanity.com/paper/2309.14246/) (2023)
- [Multi-Robot Collision Avoidance under Uncertainty with Probabilistic Safety Barrier Certificates](https://mlsanity.com/paper/1912.09957/) (2019)
- [Stochastic Model Predictive Control with a Safety Guarantee for Automated Driving: Extended Version](https://mlsanity.com/paper/2009.09381/) (2020)
- [Path Integral Control and State Dependent Feedback](https://mlsanity.com/paper/1406.4026/) (2014)
- [Probabilistic Safety-Assured Adaptive Merging Control for Autonomous Vehicles](https://mlsanity.com/paper/2104.14159/) (2021)
- [Safety-Aware Optimal Control of Stochastic Systems Using Conditional Value-at-Risk](https://mlsanity.com/paper/1802.07903/) (2018)
- [Risk-Sensitive Motion Planning using Entropic Value-at-Risk](https://mlsanity.com/paper/2011.11211/) (2020)

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

- [Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems](https://mlsanity.com/paper/2407.08868/) (2024)

## Abstract (arXiv)

This paper addresses the design of safety certificates for stochastic systems, with a focus on ensuring long-term safety through fast real-time control. In stochastic environments, set invariance-based methods that restrict the probability of risk events in infinitesimal time intervals may exhibit significant long-term risks due to cumulative uncertainties/risks. On the other hand, reachability-based approaches that account for the long-term future may require prohibitive computation in real-time decision making. To overcome this challenge involving stringent long-term safety vs. computation tradeoffs, we first introduce a novel technique termed 'probabilistic invariance'. This technique characterizes the invariance conditions of the probability of interest. When the target probability is defined using long-term trajectories, this technique can be used to design myopic conditions/controllers with assured long-term safe probability. Then, we integrate this technique into safe control and learning. The proposed control methods efficiently assure long-term safety using neural networks or model predictive controllers with short outlook horizons. The proposed learning methods can be used to guarantee long-term safety during and after training. Finally, we demonstrate the performance of the proposed techniques in numerical simulations.