# Trajectory Modeling via Random Utility Inverse Reinforcement Learning

arXiv: https://arxiv.org/abs/2105.12092 · HTML: https://mlsanity.com/paper/2105.12092/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation and offline RL for driving, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 1 of its 46 references that are in the map.
- First posted on arXiv 25 May 2021.

## Placed in

- Offline RL and imitation learning from data / [Imitation and offline RL for driving](https://mlsanity.com/offlinerl/imitation-and-offline-rl-for-driving/)

## Builds on (most cited first, 1 of 1)

- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)

## Abstract (arXiv)

We consider the problem of modeling trajectories of drivers in a road network from the perspective of inverse reinforcement learning. Cars are detected by sensors placed on sparsely distributed points on the street network of a city. As rational agents, drivers are trying to maximize some reward function unknown to an external observer. We apply the concept of random utility from econometrics to model the unknown reward function as a function of observed and unobserved features. In contrast to current inverse reinforcement learning approaches, we do not assume that agents act according to a stochastic policy; rather, we assume that agents act according to a deterministic optimal policy and show that randomness in data arises because the exact rewards are not fully observed by an external observer. We introduce the concept of extended state to cope with unobserved features and develop a Markov decision process formulation of drivers decisions. We present theoretical results which guarantee the existence of solutions and show that maximum entropy inverse reinforcement learning is a particular case of our approach. Finally, we illustrate Bayesian inference on model parameters through a case study with real trajectory data from a large city in Brazil.