The paper proposes a new variant of DeepReach, called ExactBC, that exactly imposes the safety constraints (i.e., the boundary conditions) during the learning process. The key idea is to represent the value function as a weighted combination of the boundary value function and the neural network output, where the neural network output is weighted by a "distance function" to the boundary. This ensures that the learned value function always satisfies the boundary conditions.
The paper first provides a background on Hamilton-Jacobi reachability analysis and the original DeepReach method. It then details the proposed ExactBC approach, including the value function approximation and the training scheme.
The authors evaluate the proposed ExactBC method on two high-dimensional reachability problems - a 6D rocket landing problem and a 9D three-vehicle collision avoidance problem. They benchmark ExactBC against the vanilla DeepReach and the DiffModel variant. The results show that ExactBC significantly outperforms the baselines in terms of the accuracy and consistency of the learned reachable tubes. Specifically, ExactBC is able to recover a much larger provably safe volume compared to the other methods, demonstrating the benefits of exactly imposing the safety constraints.
The paper also highlights that the proposed pretraining strategy further stabilizes the training process and reduces the dependence on the neural network's weight initialization.
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arxiv.org
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by Aditya Singh... ב- arxiv.org 04-02-2024
https://arxiv.org/pdf/2404.00814.pdfשאלות מעמיקות