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).

翻译：我们提出了MMD-OPT：一种在动态障碍物任意预测分布下最小化碰撞风险的样本高效方法。MMD-OPT基于再生核希尔伯特空间中的分布嵌入及其相关的最大均值差异。我们展示了如何利用这两个概念来定义一个用于碰撞风险估计的样本高效代理。我们进行了广泛的仿真实验，在合成数据集和真实世界数据集上验证了MMD-OPT的有效性。重要的是，我们证明，与基于条件风险价值的流行替代方法相比，采用我们基于MMD的碰撞风险代理进行轨迹优化，能够在低样本条件下生成更安全的轨迹。