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arXiv · 2412.09121

MMD-OPT : Maximum Mean Discrepancy Based Sample Efficient Collision Risk Minimization for Autonomous Driving

Basant Sharma·Arun Kumar Singh
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Abstract

We propose MMD-OPT: a sample-efficient approach for minimizing the risk of collision under arbitrary prediction distribution of the dynamic obstacles. MMD-OPT is based on embedding distribution in Reproducing Kernel Hilbert Space (RKHS) and the associated Maximum Mean Discrepancy (MMD). We show how these two concepts can be used to define a sample efficient surrogate for collision risk estimate. We perform extensive simulations to validate the effectiveness of MMD-OPT on both synthetic and real-world datasets. Importantly, we show that trajectory optimization with our MMD-based collision risk surrogate leads to safer trajectories at low sample regimes than popular alternatives based on Conditional Value at Risk (CVaR).

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Basant Sharma, Arun Kumar Singh. 2024-12-12. MMD-OPT : Maximum Mean Discrepancy Based Sample Efficient Collision Risk Minimization for Autonomous Driving. https://arxiv.org/abs/2412.09121

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