mlsanityData to 14 Oct 2026

Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control

arXiv 2109.08947 ↗First posted 18 Sep 2021cs.AIcited by 12

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Abstract (arXiv)

We present an historical overview about the connections between the analysis of risk and the control of autonomous systems. We offer two main contributions. Our first contribution is to propose three overlapping paradigms to classify the vast body of literature: the worst-case, risk-neutral, and risk-averse paradigms. We consider an appropriate assessment for the risk of an autonomous system to depend on the application at hand. In contrast, it is typical to assess risk using an expectation, variance, or probability alone. Our second contribution is to unify the concepts of risk and autonomous systems. We achieve this by connecting approaches for quantifying and optimizing the risk that arises from a system's behaviour across academic fields. The survey is highly multidisciplinary. We include research from the communities of reinforcement learning, stochastic and robust control theory, operations research, and formal verification. We describe both model-based and model-free methods, with emphasis on the former. Lastly, we highlight fruitful areas for further research. A key direction is to blend risk-averse model-based and model-free methods to enhance the real-time adaptive capabilities of systems to improve human and environmental welfare.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 47 of its 167 references that are in the map. First posted on arXiv 18 Sep 2021.

Builds on

47 of 167 references.

References · 47

  1. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 371
  2. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  3. 2018A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progresscited by 298
  4. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 291
  5. 2019End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Taskscited by 289
  6. 2015Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approachcited by 170
  7. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 163
  8. 2013Risk-sensitive Reinforcement Learningcited by 130
  9. 2018A predictive safety filter for learning-based control of constrained nonlinear dynamical systemscited by 118
  10. 2013Data-Driven Robust Optimizationcited by 85
  11. 2018Verisig: verifying safety properties of hybrid systems with neural network controllerscited by 84
  12. 2015Safe Controller Optimization for Quadrotors with Gaussian Processescited by 78
35 more
  1. 2016Safe Exploration in Finite Markov Decision Processes with Gaussian Processescited by 75
  2. 2020Chasing Carbon: The Elusive Environmental Footprint of Computingcited by 72
  3. 2019Learning for Safety-Critical Control with Control Barrier Functionscited by 69
  4. 2017How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Roboticscited by 59
  5. 2014A Learning Based Approach to Control Synthesis of Markov Decision Processes for Linear Temporal Logic Specificationscited by 49
  6. 2014Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraintscited by 44
  7. 2014Safe Exploration of State and Action Spaces in Reinforcement Learningcited by 38
  8. 2018Wasserstein Distributionally Robust Stochastic Control: A Data-Driven Approachcited by 29
  9. 2019ReachNN: Reachability Analysis of Neural-Network Controlled Systemscited by 26
  10. 2013The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violationscited by 24
  11. 2019Probabilistic model predictive safety certification for learning-based controlcited by 22
  12. 2017DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimizationcited by 19
  13. 2016Decomposition of Reachable Sets and Tubes for a Class of Nonlinear Systemscited by 18
  14. 2020Markov Decision Processes with Recursive Risk Measurescited by 18
  15. 2019A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systemscited by 15
  16. 2021Risk-sensitive safety analysis using Conditional Value-at-Riskcited by 14
  17. 2020Risk-Averse Learning by Temporal Difference Methodscited by 13
  18. 2020Minimizing Spectral Risk Measures Applied to Markov Decision Processescited by 12
  19. 2018Stochastic Approximation for Risk-aware Markov Decision Processescited by 10
  20. 2018Safety-Aware Optimal Control of Stochastic Systems Using Conditional Value-at-Riskcited by 8
  21. 2019Control of Mobile Robots Using Barrier Functions Under Temporal Logic Specificationscited by 8
  22. 2017A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithmscited by 6
  23. 2017A dynamic game approach to distributionally robust safety specifications for stochastic systemscited by 5
  24. 2021Reactive and Risk-Aware Control for Signal Temporal Logiccited by 5
  25. 2021Toward a Scalable Upper Bound for a CVaR-LQ Problemcited by 4
  26. 2021STL Robustness Risk over Discrete-Time Stochastic Processescited by 4
  27. 2021On Optimizing the Conditional Value-at-Risk of a Maximum Cost for Risk-Averse Safety Analysiscited by 4
  28. 2015A variational formula for risk-sensitive rewardcited by 3
  29. 2015Synthesis of separable controlled invariant sets for modular local control designcited by 3
  30. 2015Conditional Value-at-Risk: Theory and Applicationscited by 3
  31. 2015Optimal Control of Conditional Value-at-Risk in Continuous Timecited by 3
  32. 2017Shrinking Horizon Model Predictive Control with Signal Temporal Logic Constraints under Stochastic Disturbancescited by 3
  33. 2021On Exponential Utility and Conditional Value-at-Risk as Risk-Averse Performance Criteriacited by 3
  34. 2020Control Design for Risk-Based Signal Temporal Logic Specificationscited by 2
  35. 2021Classical Risk-Averse Control for a Finite-Horizon Borel Modelcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 2; 2024: 2; 2025: 3; 2026: 3.

12 papers.

  1. 2022RAP: Risk-Aware Prediction for Robust Planningcited by 12
  2. 2022Risk Verification of Stochastic Systems with Neural Network Controllerscited by 6
  3. 2024Q-learning for Quantile MDPs: A Decomposition, Performance, and Convergence Analysiscited by 6
  4. 2023Time-uniform confidence bands for the CDF under nonstationaritycited by 2
  5. 2023Eliciting Risk Aversion with Inverse Reinforcement Learning via Interactive Questioningcited by 2
  6. 2024Burning RED: Unlocking Subtask-Driven Reinforcement Learning and Risk-Awareness in Average-Reward Markov Decision Processescited by 2
  7. 2025Risk-aware Direct Preference Optimization under Nested Risk Measurecited by 2
  8. 2025Risk-Sensitive Agent Compositionscited by 1
  9. 2025Constrained Language Model Policy Optimization via Risk-aware Stepwise Alignmentcited by 0
  10. 2026Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinitycited by 0
  11. 2026Online Policy Evaluation for MDPs with Dynamic UBSR Measurescited by 0
  12. 2026Adaptive Finite-Budget Training for CVaR Risk-Aware Q-Learningcited by 0