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

arXiv: https://arxiv.org/abs/2412.09121 · HTML: https://mlsanity.com/paper/2412.09121/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 51 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 28 of 28)

- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [STORM: An Integrated Framework for Fast Joint-Space Model-Predictive Control for Reactive Manipulation](https://mlsanity.com/paper/2104.13542/) (2021)
- [DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehicles](https://mlsanity.com/paper/2212.06437/) (2022)
- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Pedestrian Trajectory Prediction with Convolutional Neural Networks](https://mlsanity.com/paper/2010.05796/) (2020)
- [Safe Trajectory Generation for Complex Urban Environments Using Spatio-temporal Semantic Corridor](https://mlsanity.com/paper/1906.09788/) (2019)
- [Optimization-Based Hierarchical Motion Planning for Autonomous Racing](https://mlsanity.com/paper/2003.04882/) (2020)
- [Model- and Acceleration-based Pursuit Controller for High-Performance Autonomous Racing](https://mlsanity.com/paper/2209.04346/) (2022)
- [RACP: Risk-Aware Contingency Planning with Multi-Modal Predictions](https://mlsanity.com/paper/2402.17387/) (2024)
- [A Real-Time Approach for Chance-Constrained Motion Planning with Dynamic Obstacles](https://mlsanity.com/paper/2001.08012/) (2020)
- [Multi-Modal Model Predictive Control through Batch Non-Holonomic Trajectory Optimization: Application to Highway Driving](https://mlsanity.com/paper/2109.10392/) (2021)
- [Provably Safe Trajectory Optimization in the Presence of Uncertain Convex Obstacles](https://mlsanity.com/paper/2003.07811/) (2020)
- [Maximum Mean Discrepancy Distributionally Robust Nonlinear Chance-Constrained Optimization with Finite-Sample Guarantee](https://mlsanity.com/paper/2204.11564/) (2022)
- [Risk-Aware Model Predictive Path Integral Control Using Conditional Value-at-Risk](https://mlsanity.com/paper/2209.12842/) (2022)
- [Risk-Averse Trajectory Optimization via Sample Average Approximation](https://mlsanity.com/paper/2307.03167/) (2023)
- [Covariance Steering for Uncertain Contact-rich Systems](https://mlsanity.com/paper/2303.13382/) (2023)
- [Solving Chance Constrained Optimization under Non-Parametric Uncertainty Through Hilbert Space Embedding](https://mlsanity.com/paper/1811.09311/) (2018)
- [Safe Motion Planning for Autonomous Driving using an Adversarial Road Model](https://mlsanity.com/paper/2005.07691/) (2020)
- [Consistent Kernel Mean Estimation for Functions of Random Variables](https://mlsanity.com/paper/1610.05950/) (2016)
- [A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control](https://mlsanity.com/paper/2001.10398/) (2020)
- [Safe Motion Planning against Multimodal Distributions based on a Scenario Approach](https://mlsanity.com/paper/2108.02753/) (2021)
- [CCO-VOXEL: Chance Constrained Optimization over Uncertain Voxel-Grid Representation for Safe Trajectory Planning](https://mlsanity.com/paper/2110.02904/) (2021)
- [Hilbert Space Embedding-based Trajectory Optimization for Multi-Modal Uncertain Obstacle Trajectory Prediction](https://mlsanity.com/paper/2310.08270/) (2023)

## Abstract (arXiv)

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).