Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loops
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913405835673600 |
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| author | Jafarpour, Saber Harapanahalli, Akash Coogan, Samuel |
| author_facet | Jafarpour, Saber Harapanahalli, Akash Coogan, Samuel |
| contents | In this paper, we propose a computationally efficient framework for interval reachability of systems with neural network controllers. Our approach leverages inclusion functions for the open-loop system and the neural network controller to embed the closed-loop system into a larger-dimensional embedding system, where a single trajectory over-approximates the original system's behavior under uncertainty. We propose two methods for constructing closed-loop embedding systems, which account for the interactions between the system and the controller in different ways. The interconnection-based approach considers the worst-case evolution of each coordinate separately by substituting the neural network inclusion function into the open-loop inclusion function. The interaction-based approach uses novel Jacobian-based inclusion functions to capture the first-order interactions between the open-loop system and the controller by leveraging state-of-the-art neural network verifiers. Finally, we implement our approach in a Python framework called ReachMM to demonstrate its efficiency and scalability on benchmarks and examples ranging to $200$ state dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loops Jafarpour, Saber Harapanahalli, Akash Coogan, Samuel Systems and Control Machine Learning Optimization and Control In this paper, we propose a computationally efficient framework for interval reachability of systems with neural network controllers. Our approach leverages inclusion functions for the open-loop system and the neural network controller to embed the closed-loop system into a larger-dimensional embedding system, where a single trajectory over-approximates the original system's behavior under uncertainty. We propose two methods for constructing closed-loop embedding systems, which account for the interactions between the system and the controller in different ways. The interconnection-based approach considers the worst-case evolution of each coordinate separately by substituting the neural network inclusion function into the open-loop inclusion function. The interaction-based approach uses novel Jacobian-based inclusion functions to capture the first-order interactions between the open-loop system and the controller by leveraging state-of-the-art neural network verifiers. Finally, we implement our approach in a Python framework called ReachMM to demonstrate its efficiency and scalability on benchmarks and examples ranging to $200$ state dimensions. |
| title | Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loops |
| topic | Systems and Control Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2307.14938 |