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

Jingqi Li, Chih Yuan Chiu, Lasse Peters, Somayeh Sojoudi, Claire Tomlin, David Fridovich-Keil

Research output: Contribution to journalConference articleScientificpeer-review


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.

Original languageEnglish
Pages (from-to)1062-1070
JournalProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Publication statusPublished - 2023
Event22nd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2023 - London, United Kingdom
Duration: 29 May 20232 Jun 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project
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.


  • Dynamic Game Theory
  • Inverse Games
  • Nash Equilibrium


Dive into the research topics of 'Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories'. Together they form a unique fingerprint.

Cite this