# Motion Forecasting via Model-Based Risk Minimization

arXiv: https://arxiv.org/abs/2409.10585 · HTML: https://mlsanity.com/paper/2409.10585/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 62 references that are in the map.
- First posted on arXiv 16 Sep 2024.

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Argoverse 2: Next Generation Datasets for Self-Driving Perception and Forecasting](https://mlsanity.com/paper/2301.00493/) (2023)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [TNT: Target-driveN Trajectory Prediction](https://mlsanity.com/paper/2008.08294/) (2020)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [DenseTNT: End-to-end Trajectory Prediction from Dense Goal Sets](https://mlsanity.com/paper/2108.09640/) (2021)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [Human Motion Trajectory Prediction: A Survey](https://mlsanity.com/paper/1905.06113/) (2019)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [TrafficSim: Learning to Simulate Realistic Multi-Agent Behaviors](https://mlsanity.com/paper/2101.06557/) (2021)
- [MotionLM: Multi-Agent Motion Forecasting as Language Modeling](https://mlsanity.com/paper/2309.16534/) (2023)
- [GOHOME: Graph-Oriented Heatmap Output for future Motion Estimation](https://mlsanity.com/paper/2109.01827/) (2021)
- [MTR++: Multi-Agent Motion Prediction with Symmetric Scene Modeling and Guided Intention Querying](https://mlsanity.com/paper/2306.17770/) (2023)
- [HOME: Heatmap Output for future Motion Estimation](https://mlsanity.com/paper/2105.10968/) (2021)
- [Implicit Latent Variable Model for Scene-Consistent Motion Forecasting](https://mlsanity.com/paper/2007.12036/) (2020)
- [Multimodal Trajectory Prediction Conditioned on Lane-Graph Traversals](https://mlsanity.com/paper/2106.15004/) (2021)
- [THOMAS: Trajectory Heatmap Output with learned Multi-Agent Sampling](https://mlsanity.com/paper/2110.06607/) (2021)
- [M2I: From Factored Marginal Trajectory Prediction to Interactive Prediction](https://mlsanity.com/paper/2202.11884/) (2022)
- [LaPred: Lane-Aware Prediction of Multi-Modal Future Trajectories of Dynamic Agents](https://mlsanity.com/paper/2104.00249/) (2021)
- [MG-GAN: A Multi-Generator Model Preventing Out-of-Distribution Samples in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2108.09274/) (2021)
- [LAformer: Trajectory Prediction for Autonomous Driving with Lane-Aware Scene Constraints](https://mlsanity.com/paper/2302.13933/) (2023)
- [UniTraj: A Unified Framework for Scalable Vehicle Trajectory Prediction](https://mlsanity.com/paper/2403.15098/) (2024)
- [Identifying Driver Interactions via Conditional Behavior Prediction](https://mlsanity.com/paper/2104.09959/) (2021)

## Built on by (most cited first, 4 of 4)

- [Stochasticity in Motion: An Information-Theoretic Approach to Trajectory Prediction](https://mlsanity.com/paper/2410.01628/) (2024)
- [ParkDiffusion: Heterogeneous Multi-Agent Multi-Modal Trajectory Prediction for Automated Parking using Diffusion Models](https://mlsanity.com/paper/2505.00586/) (2025)
- [ParkDiffusion++: Ego Intention Conditioned Joint Multi-Agent Trajectory Prediction for Automated Parking using Diffusion Models](https://mlsanity.com/paper/2602.20923/) (2026)
- [Class-Incremental Motion Forecasting](https://mlsanity.com/paper/2603.09420/) (2026)

## Abstract (arXiv)

Forecasting the future trajectories of surrounding agents is crucial for autonomous vehicles to ensure safe, efficient, and comfortable route planning. While model ensembling has improved prediction accuracy in various fields, its application in trajectory prediction is limited due to the multi-modal nature of predictions. In this paper, we propose a novel sampling method applicable to trajectory prediction based on the predictions of multiple models. We first show that conventional sampling based on predicted probabilities can degrade performance due to missing alignment between models. To address this problem, we introduce a new method that generates optimal trajectories from a set of neural networks, framing it as a risk minimization problem with a variable loss function. By using state-of-the-art models as base learners, our approach constructs diverse and effective ensembles for optimal trajectory sampling. Extensive experiments on the nuScenes prediction dataset demonstrate that our method surpasses current state-of-the-art techniques, achieving top ranks on the leaderboard. We also provide a comprehensive empirical study on ensembling strategies, offering insights into their effectiveness. Our findings highlight the potential of advanced ensembling techniques in trajectory prediction, significantly improving predictive performance and paving the way for more reliable predicted trajectories.