# A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems

arXiv: https://arxiv.org/abs/1902.11277 · HTML: https://mlsanity.com/paper/1902.11277/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2019.

## Built on by (most cited first, 15 of 15)

- [On Dynamic Programming Decompositions of Static Risk Measures in Markov Decision Processes](https://mlsanity.com/paper/2304.12477/) (2023)
- [Maximum Likelihood Constraint Inference from Stochastic Demonstrations](https://mlsanity.com/paper/2102.12554/) (2021)
- [Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control](https://mlsanity.com/paper/2109.08947/) (2021)
- [Risk-Averse Stochastic Shortest Path Planning](https://mlsanity.com/paper/2103.14727/) (2021)
- [Game-Theoretic Planning for Autonomous Driving among Risk-Aware Human Drivers](https://mlsanity.com/paper/2205.00562/) (2022)
- [Risk Verification of Stochastic Systems with Neural Network Controllers](https://mlsanity.com/paper/2209.09881/) (2022)
- [STL Robustness Risk over Discrete-Time Stochastic Processes](https://mlsanity.com/paper/2104.01503/) (2021)
- [A Generalizable Physics-informed Learning Framework for Risk Probability Estimation](https://mlsanity.com/paper/2305.06432/) (2023)
- [Risk-averse Learning with Non-Stationary Distributions](https://mlsanity.com/paper/2404.02988/) (2024)
- [A Risk-Averse Preview-based Q-Learning Algorithm: Application to Highway Driving of Autonomous Vehicles](https://mlsanity.com/paper/2112.03232/) (2021)
- [Physics-informed RL for Maximal Safety Probability Estimation](https://mlsanity.com/paper/2403.16391/) (2024)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [On the Fundamental Limitations of Dual Static CVaR Decompositions in Markov Decision Processes](https://mlsanity.com/paper/2507.14005/) (2025)
- [Uncertainty Principles in Risk-Aware Statistical Estimation](https://mlsanity.com/paper/2104.14283/) (2021)
- [Actor-Critic Learning for Risk-Constrained Linear Quadratic Regulation](https://mlsanity.com/paper/2510.22267/) (2025)

## Abstract (arXiv)

A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set, and provide theoretical arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis).