# Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data

arXiv: https://arxiv.org/abs/2212.06253 · HTML: https://mlsanity.com/paper/2212.06253/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 12 Dec 2022.

## Builds on (most cited first, 23 of 23)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Residual Reinforcement Learning for Robot Control](https://mlsanity.com/paper/1812.03201/) (2018)
- [TossingBot: Learning to Throw Arbitrary Objects with Residual Physics](https://mlsanity.com/paper/1903.11239/) (2019)
- [Risk-sensitive Reinforcement Learning](https://mlsanity.com/paper/1311.2097/) (2013)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Safe Learning of Quadrotor Dynamics Using Barrier Certificates](https://mlsanity.com/paper/1710.05472/) (2017)
- [Actively Learning Gaussian Process Dynamics](https://mlsanity.com/paper/1911.09946/) (2019)
- [Autonomous Spot: Long-Range Autonomous Exploration of Extreme Environments with Legged Locomotion](https://mlsanity.com/paper/2010.09259/) (2020)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [Safe Learning and Optimization Techniques: Towards a Survey of the State of the Art](https://mlsanity.com/paper/2101.09505/) (2021)
- [Input-to-State Safety With Control Barrier Functions](https://mlsanity.com/paper/1803.03035/) (2018)
- [Constrained Risk-Averse Markov Decision Processes](https://mlsanity.com/paper/2012.02423/) (2020)
- [Risk-Sensitive Motion Planning using Entropic Value-at-Risk](https://mlsanity.com/paper/2011.11211/) (2020)
- [Safe Controller Synthesis with Tunable Input-to-State Safe Control Barrier Functions](https://mlsanity.com/paper/2103.08041/) (2021)
- [Reactive and Risk-Aware Control for Signal Temporal Logic](https://mlsanity.com/paper/2108.13490/) (2021)
- [Verifying Safe Transitions between Dynamic Motion Primitives on Legged Robots](https://mlsanity.com/paper/2106.10310/) (2021)
- [Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification](https://mlsanity.com/paper/2204.09833/) (2022)
- [Risk-Averse Planning via CVaR Barrier Functions: Application to Bipedal Robot Locomotion](https://mlsanity.com/paper/2011.01578/) (2020)
- [Safety-Critical Controller Verification via Sim2Real Gap Quantification](https://mlsanity.com/paper/2209.09337/) (2022)

## Abstract (arXiv)

Recent advances in safety-critical risk-aware control are predicated on apriori knowledge of the disturbances a system might face. This paper proposes a method to efficiently learn these disturbances online, in a risk-aware context. First, we introduce the concept of a Surface-at-Risk, a risk measure for stochastic processes that extends Value-at-Risk -- a commonly utilized risk measure in the risk-aware controls community. Second, we model the norm of the state discrepancy between the model and the true system evolution as a scalar-valued stochastic process and determine an upper bound to its Surface-at-Risk via Gaussian Process Regression. Third, we provide theoretical results on the accuracy of our fitted surface subject to mild assumptions that are verifiable with respect to the data sets collected during system operation. Finally, we experimentally verify our procedure by augmenting a drone's controller and highlight performance increases achieved via our risk-aware approach after collecting less than a minute of operating data.