Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories

Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories

Li, Jingqi (University of California)
Chiu, Chih Yuan (University of California)
Peters, L. (TU Delft Learning & Autonomous Control)
Sojoudi, Somayeh (University of California)
Tomlin, Claire (University of California)
Fridovich-Keil, David (The University of Texas at Austin)

2023

In multi-agent dynamic games, the Nash equilibrium state trajectory of each agent is determined by its cost function and the information pattern of the game. However, the cost and trajectory of each agent may be unavailable to the other agents. Prior work on using partial observations to infer the costs in dynamic games assumes an open-loop information pattern. In this work, we demonstrate that the feedback Nash equilibrium concept is more expressive and encodes more complex behavior. It is desirable to develop specific tools for inferring players' objectives in feedback games. Therefore, we consider the dynamic game cost inference problem under the feedback information pattern, using only partial state observations and incomplete trajectory data. To this end, we first propose an inverse feedback game loss function, whose minimizer yields a feedback Nash equilibrium state trajectory closest to the observation data. We characterize the landscape and differentiability of the loss function. Given the difficulty of obtaining the exact gradient, our main contribution is an efficient gradient approximator, which enables a novel inverse feedback game solver that minimizes the loss using first-order optimization. In thorough empirical evaluations, we demonstrate that our algorithm converges reliably and has better robustness and generalization performance than the open-loop baseline method when the observation data reflects a group of players acting in a feedback Nash game.

Dynamic Game Theory
Inverse Games
Nash Equilibrium

http://resolver.tudelft.nl/uuid:1ae6ef3a-b7ed-411f-b623-dbe9df7bbbf5

10.5555/3545946.3598746

2023-11-30

1548-8403

Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS, 1062-1070

22nd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2023, 2023-05-29 → 2023-06-02, London, United Kingdom

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2023 Jingqi Li, Chih Yuan Chiu, L. Peters, Somayeh Sojoudi, Claire Tomlin, David Fridovich-Keil