# Interactive Trajectory Planning with Learning-based Distributionally Robust Model Predictive Control and Markov Systems

arXiv: https://arxiv.org/abs/2605.07768 · HTML: https://mlsanity.com/paper/2605.07768/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 8 of 8)

- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Interactive multi-modal motion planning with Branch Model Predictive Control](https://mlsanity.com/paper/2109.05128/) (2021)
- [Stochastic MPC with Multi-modal Predictions for Traffic Intersections](https://mlsanity.com/paper/2109.09792/) (2021)
- [A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems](https://mlsanity.com/paper/2106.00561/) (2021)
- [Risk-averse risk-constrained optimal control](https://mlsanity.com/paper/1903.06749/) (2019)
- [Interaction-Aware Trajectory Prediction and Planning in Dense Highway Traffic using Distributed Model Predictive Control](https://mlsanity.com/paper/2308.13053/) (2023)
- [Combined Stochastic and Robust Optimization for Electric Autonomous Mobility-on-Demand with Nested Benders Decomposition](https://mlsanity.com/paper/2508.19933/) (2025)
- [Tight Collision Avoidance for Stochastic Optimal Control: with Applications in Learning-based, Interactive Motion Planning](https://mlsanity.com/paper/2510.25324/) (2025)

## Abstract (arXiv)

We investigate interactive trajectory planning subject to uncertainty in the decisions of surrounding agents. To control the ego-agent, we aim to first learn the decision distribution and solve a Stochastic Model Predictive Control (SMPC) problem. To account for errors in the learned distribution, we show that it is possible to utilize Probably Approximately Correct (PAC) learning in combination with Distributionally Robust (DR) optimization to obtain a solution which accounts for the errors induced by the learning model. The results indicate that our PAC learning-based DR-MPC framework provides a method to interpolate between a robust MPC and an omnipotent SMPC, based on the available number of samples.