Unsafe Probabilities and Risk Contours for Stochastic Processes using Convex Optimization
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912984445485056 |
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| author | Miller, Jared Tacchi, Matteo Henrion, Didier Sznaier, Mario |
| author_facet | Miller, Jared Tacchi, Matteo Henrion, Didier Sznaier, Mario |
| contents | This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of infinite-dimensional linear programs in occupation measures and continuous functions. This convex relaxation is nonconservative (to the true probability of unsafety) under compactness and regularity conditions in dynamics. The continuous-function linear program is linked to existing probability-certifying barrier certificates of safety. Risk contours for initial conditions of the stochastic process may be generated by suitably modifying the objective of the continuous-function program, forming an interpretable and visual representation of stochastic safety for test initial conditions. All infinite-dimensional linear programs are truncated to finite dimension by the Moment-Sum-of-Squares hierarchy of semidefinite programs. Unsafe-probability estimation and risk contours are generated for example stochastic processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00815 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unsafe Probabilities and Risk Contours for Stochastic Processes using Convex Optimization Miller, Jared Tacchi, Matteo Henrion, Didier Sznaier, Mario Optimization and Control Systems and Control This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of infinite-dimensional linear programs in occupation measures and continuous functions. This convex relaxation is nonconservative (to the true probability of unsafety) under compactness and regularity conditions in dynamics. The continuous-function linear program is linked to existing probability-certifying barrier certificates of safety. Risk contours for initial conditions of the stochastic process may be generated by suitably modifying the objective of the continuous-function program, forming an interpretable and visual representation of stochastic safety for test initial conditions. All infinite-dimensional linear programs are truncated to finite dimension by the Moment-Sum-of-Squares hierarchy of semidefinite programs. Unsafe-probability estimation and risk contours are generated for example stochastic processes. |
| title | Unsafe Probabilities and Risk Contours for Stochastic Processes using Convex Optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2401.00815 |