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

2025-08-27

AI Summary

Learning implicit constraints from local generalized Nash equilibrium (GNE) demonstration data in multi-agent dynamic games remains challenging, especially under nonlinear dynamics and mixed convex/non-convex safety constraints. Method: We propose an inverse dynamic game-based framework for parametric constraint learning. Our approach encodes the KKT conditions of Nash equilibria as a mixed-integer linear program (MILP), enabling inner approximations of both convex and non-convex safe/unsafe sets—even under nonlinear system dynamics—for the first time. Contribution/Results: We theoretically prove that the learned constraint set is strictly contained within the true feasible set and characterize the learnability boundary under GNE demonstrations. Experiments on simulation and real-world robotic platforms demonstrate accurate recovery of diverse constraints and generation of robust, interaction-compliant motion trajectories. The method significantly improves planning safety and generalization in complex multi-agent scenarios.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We present an inverse dynamic game-based algorithm to learn parametric constraints from a given dataset of local generalized 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 Nash stationarity of the interaction demonstrations. We establish theoretical guarantees that our method learns inner approximations of the true safe and unsafe sets, as well as limitations of constraint learnability from demonstrations of Nash equilibrium interactions. 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 proved capable of inferring constraints and designing interactive motion plans for various classes of constraints, both convex and non-convex, from interaction demonstrations of agents with nonlinear dynamics.

Problem

• Learning parametric constraints from multi-agent Nash equilibrium demonstrations
• Recovering constraint sets via MILP encoding of KKT conditions
• Designing interactive motion plans that robustly satisfy learned constraints

Innovation

• Inverse dynamic game algorithm learning constraints
• MILP encoding KKT conditions for Nash equilibrium
• Recovering constraint approximations from interaction demonstrations