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

Akella, Prithvi and Dixit, Anushri and Ahmadi, Mohamadreza and Burdick, Joel W. and Ames, Aaron D. (2022) Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220714-194303859

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Abstract

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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://doi.org/10.48550/arXiv.2204.09833arXivDiscussion Paper
ORCID:
AuthorORCID
Akella, Prithvi0000-0003-4375-0015
Dixit, Anushri0000-0002-9698-2189
Ahmadi, Mohamadreza0000-0003-1447-3012
Burdick, Joel W.0000-0002-3091-540X
Ames, Aaron D.0000-0003-0848-3177
Additional Information:Attribution 4.0 International (CC BY 4.0) This work was supported by the AFOSR Test and Evaluation Program, grant FA9550-19-1-0302.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0302
Record Number:CaltechAUTHORS:20220714-194303859
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220714-194303859
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115563
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:15 Jul 2022 22:36
Last Modified:15 Jul 2022 22:36

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