# Inferring Objectives in Continuous Dynamic Games from Noise-Corrupted Partial State Observations

arXiv: https://arxiv.org/abs/2106.03611 · HTML: https://mlsanity.com/paper/2106.03611/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2021.

## Built on by (most cited first, 13 of 13)

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- [On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions](https://mlsanity.com/paper/2308.16539/) (2023)
- [Distributed Differentiable Dynamic Game for Multi-robot Coordination](https://mlsanity.com/paper/2207.08892/) (2022)
- [Active Inverse Learning in Stackelberg Trajectory Games](https://mlsanity.com/paper/2308.08017/) (2023)
- [CV-MOS: A Cross-View Model for Motion Segmentation](https://mlsanity.com/paper/2408.13790/) (2024)
- [Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions](https://mlsanity.com/paper/2508.19945/) (2025)
- [Multi-Agent Inverse Q-Learning from Demonstrations](https://mlsanity.com/paper/2503.04679/) (2025)
- [PACE: A Framework for Learning and Control in Linear Incomplete-Information Differential Games](https://mlsanity.com/paper/2504.17128/) (2025)

## Abstract (arXiv)

Robots and autonomous systems must interact with one another and their environment to provide high-quality services to their users. Dynamic game theory provides an expressive theoretical framework for modeling scenarios involving multiple agents with differing objectives interacting over time. A core challenge when formulating a dynamic game is designing objectives for each agent that capture desired behavior. In this paper, we propose a method for inferring parametric objective models of multiple agents based on observed interactions. Our inverse game solver jointly optimizes player objectives and continuous-state estimates by coupling them through Nash equilibrium constraints. Hence, our method is able to directly maximize the observation likelihood rather than other non-probabilistic surrogate criteria. Our method does not require full observations of game states or player strategies to identify player objectives. Instead, it robustly recovers this information from noisy, partial state observations. As a byproduct of estimating player objectives, our method computes a Nash equilibrium trajectory corresponding to those objectives. Thus, it is suitable for downstream trajectory forecasting tasks. We demonstrate our method in several simulated traffic scenarios. Results show that it reliably estimates player objectives from a short sequence of noise-corrupted partial state observations. Furthermore, using the estimated objectives, our method makes accurate predictions of each player's trajectory.