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

## TL;DR

This paper introduces an inverse dynamic game algorithm that learns constraints from multi-agent local Nash interactions, enabling the design of safe motion plans with theoretical guarantees and practical effectiveness.

## Contribution

It develops a MILP-based method to recover constraints from local Nash equilibrium data, providing guarantees and applicability to nonlinear multi-agent systems.

## Key findings

- Successfully infers constraints from demonstrations of agents with nonlinear dynamics.
- Designs motion plans that satisfy learned constraints robustly.
- Achieves accurate constraint learning and safe planning in simulations and hardware.

## Abstract

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.