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

2024-12-12

arXiv.org

AI Summary

Reliable collision risk assessment in autonomous driving is challenging due to unknown prediction distributions of dynamic obstacles and extremely limited available samples (<50). Method: We propose a sample-efficient, differentiable risk minimization framework. Its core innovation is the first integration of Maximum Mean Discrepancy (MMD) into trajectory optimization: leveraging embeddings in a Reproducing Kernel Hilbert Space (RKHS), we construct a distribution-aware risk surrogate function that yields unbiased, low-variance estimates for arbitrary prediction distributions. This surrogate is differentiable and exhibits low sample dependency, enabling gradient-based end-to-end trajectory optimization. Results: Experiments on synthetic and real-world datasets show that our method achieves significantly lower collision rates than CVaR-based baselines under identical sample budgets; in few-shot regimes, safety performance improves by up to 37%, while maintaining computational efficiency and theoretical rigor.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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).

Problem

• Minimize collision risk in autonomous driving
• Efficiently estimate collision risk using MMD
• Improve trajectory safety with MMD-based optimization

Innovation

• MMD-OPT minimizes collision risk efficiently
• Uses RKHS embedding and MMD
• Sample-efficient surrogate for collision risk