# Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions

arXiv: https://arxiv.org/abs/2508.19945 · HTML: https://mlsanity.com/paper/2508.19945/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Builds on (most cited first, 18 of 18)

- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Games](https://mlsanity.com/paper/1909.04694/) (2019)
- [Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions](https://mlsanity.com/paper/2110.01027/) (2021)
- [LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planning](https://mlsanity.com/paper/2011.08152/) (2020)
- [ALGAMES: A Fast Augmented Lagrangian Solver for Constrained Dynamic Games](https://mlsanity.com/paper/2104.08452/) (2021)
- [Maximum Likelihood Constraint Inference from Stochastic Demonstrations](https://mlsanity.com/paper/2102.12554/) (2021)
- [Inferring Objectives in Continuous Dynamic Games from Noise-Corrupted Partial State Observations](https://mlsanity.com/paper/2106.03611/) (2021)
- [Learning Constraints from Locally-Optimal Demonstrations under Cost Function Uncertainty](https://mlsanity.com/paper/2001.09336/) (2020)
- [Contingency Games for Multi-Agent Interaction](https://mlsanity.com/paper/2304.05483/) (2023)
- [Learning Parametric Constraints in High Dimensions from Demonstrations](https://mlsanity.com/paper/1910.03477/) (2019)
- [Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectories](https://mlsanity.com/paper/2107.04926/) (2021)
- [Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories](https://mlsanity.com/paper/2301.01398/) (2023)
- [Gaussian Process Constraint Learning for Scalable Chance-Constrained Motion Planning from Demonstrations](https://mlsanity.com/paper/2112.04612/) (2021)
- [Newton's Method and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games](https://mlsanity.com/paper/1906.09097/) (2019)
- [Discretizing Dynamics for Maximum Likelihood Constraint Inference](https://mlsanity.com/paper/2109.04874/) (2021)
- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [Leadership Inference for Multi-Agent Interactions](https://mlsanity.com/paper/2310.18171/) (2023)
- [Inferring Foresightedness in Dynamic Noncooperative Games](https://mlsanity.com/paper/2412.01017/) (2024)

## Built on by (most cited first, 1 of 1)

- [Watch, Infer, Coordinate: Inferring Robot Partner Constraints for Zero-Shot Coordination](https://mlsanity.com/paper/2610.02170/) (2026)

## Abstract (arXiv)

We present an inverse dynamic game-based algorithm to learn parametric constraints from a given dataset of local Nash equilibrium interactions between multiple agents. Specifically, we introduce mixed-integer linear programs (MILP) encoding the Karush-Kuhn-Tucker (KKT) conditions of the interacting agents, which recover constraints consistent with the local Nash stationarity of the interaction demonstrations. We establish theoretical guarantees that our method learns inner approximations of the true safe and unsafe sets. We also use the interaction constraints recovered by our method to design motion plans that robustly satisfy the underlying constraints. Across simulations and hardware experiments, our methods accurately inferred constraints and designed safe interactive motion plans for various classes of constraints, both convex and non-convex, from interaction demonstrations of agents with nonlinear dynamics.