# Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification

arXiv: https://arxiv.org/abs/2204.09833 · HTML: https://mlsanity.com/paper/2204.09833/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 18 of 18)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Risk-sensitive Reinforcement Learning](https://mlsanity.com/paper/1311.2097/) (2013)
- [Sim2real transfer learning for 3D human pose estimation: motion to the rescue](https://mlsanity.com/paper/1907.02499/) (2019)
- [A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical Systems](https://mlsanity.com/paper/2005.02979/) (2020)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Adaptive Stress Testing with Reward Augmentation for Autonomous Vehicle Validation](https://mlsanity.com/paper/1908.01046/) (2019)
- [Robustness of Control Barrier Functions for Safety Critical Control](https://mlsanity.com/paper/1612.01554/) (2016)
- [Distribution oblivious, risk-aware algorithms for multi-armed bandits with unbounded rewards](https://mlsanity.com/paper/1906.00569/) (2019)
- [PAC-Bayesian Bound for the Conditional Value at Risk](https://mlsanity.com/paper/2006.14763/) (2020)
- [Reinforcement Learning for POMDP: Partitioned Rollout and Policy Iteration with Application to Autonomous Sequential Repair Problems](https://mlsanity.com/paper/2002.04175/) (2020)
- [Risk-Averse Stochastic Shortest Path Planning](https://mlsanity.com/paper/2103.14727/) (2021)
- [A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms](https://mlsanity.com/paper/1703.01029/) (2017)
- [Adaptive Stress Testing without Domain Heuristics using Go-Explore](https://mlsanity.com/paper/2004.04292/) (2020)
- [A Scenario Approach to Risk-Aware Safety-Critical System Verification](https://mlsanity.com/paper/2203.02595/) (2022)

## Built on by (most cited first, 3 of 3)

- [How Generalizable Is My Behavior Cloning Policy? A Statistical Approach to Trustworthy Performance Evaluation](https://mlsanity.com/paper/2405.05439/) (2024)
- [Verifiable Learned Behaviors via Motion Primitive Composition: Applications to Scooping of Granular Media](https://mlsanity.com/paper/2309.14894/) (2023)
- [Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data](https://mlsanity.com/paper/2212.06253/) (2022)

## Abstract (arXiv)

The dramatic increase of autonomous systems subject to variable environments has given rise to the pressing need to consider risk in both the synthesis and verification of policies for these systems. This paper aims to address a few problems regarding risk-aware verification and policy synthesis, by first developing a sample-based method to bound the risk measure evaluation of a random variable whose distribution is unknown. These bounds permit us to generate high-confidence verification statements for a large class of robotic systems. Second, we develop a sample-based method to determine solutions to non-convex optimization problems that outperform a large fraction of the decision space of possible solutions. Both sample-based approaches then permit us to rapidly synthesize risk-aware policies that are guaranteed to achieve a minimum level of system performance. To showcase our approach in simulation, we verify a cooperative multi-agent system and develop a risk-aware controller that outperforms the system's baseline controller. We also mention how our approach can be extended to account for any g-entropic risk measure - the subset of coherent risk measures on which we focus.