# Beyond Waypoint Regression: Query-Based Cost Learning over Reachable Ego Futures for End-to-End Driving

arXiv: https://arxiv.org/abs/2610.08123 · HTML: https://mlsanity.com/paper/2610.08123/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation-learning end-to-end planners, one of 9 directions in End-to-end autonomous driving.
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Placed in

- End-to-end autonomous driving / [Imitation-learning end-to-end planners](https://mlsanity.com/driving/imitation-learning-end-to-end-planners/)

## Builds on (most cited first, 7 of 7)

- [MapTR: Structured Modeling and Learning for Online Vectorized HD Map Construction](https://mlsanity.com/paper/2208.14437/) (2022)
- [Maximum Entropy Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/1507.04888/) (2015)
- [Alpamayo-R1: Bridging Reasoning and Action Prediction for Generalizable Autonomous Driving in the Long Tail](https://mlsanity.com/paper/2511.00088/) (2025)
- [DriveTransformer: Unified Transformer for Scalable End-to-End Autonomous Driving](https://mlsanity.com/paper/2503.07656/) (2025)
- [Explaining How a Deep Neural Network Trained with End-to-End Learning Steers a Car](https://mlsanity.com/paper/1704.07911/) (2017)
- [SparseAD: Sparse Query-Centric Paradigm for Efficient End-to-End Autonomous Driving](https://mlsanity.com/paper/2404.06892/) (2024)
- [Beyond Imitation: Learning Safe End-to-End Autonomous Driving from Hard Negatives](https://mlsanity.com/paper/2605.19771/) (2026)

## Abstract (arXiv)

End-to-end planners based on waypoint regression achieve strong open-loop accuracy, but they primarily learn to mimic expert geometry and remain difficult to adapt to deployment-time safety constraints. We propose a query-based cost-learning framework that estimates bounded costs for dynamically reachable ego trajectory queries, rather than dense BEV cells or a small regressed trajectory set. Compact joint scene tokens capture coherent multimodal agent futures, while contingency-aware cost aggregation and cost-guided intra-cluster MPPI mixing convert the learned cost topology into feasible ego plans. On nuScenes, our method improves over prior cost-estimation planners such as ST-P3 and NMP, outperforms most regression baselines in collision rate, while remaining competitive in L2, and retaining an interpretable cost interface. On real-world driving logs, the proposed planner reduces collision rates compared with SparseDrive and Alpamayo without fine-tuning, while maintaining a diverse set of candidate trajectories.