mlsanityData to 7 Oct 2026

On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions

arXiv 2308.16539 ↗First posted 31 Aug 2023cs.RO cs.AI cs.GTcited by 4

Not on the map. Why?

Abstract (arXiv)

Game theory offers an interpretable mathematical framework for modeling multi-agent interactions. However, its applicability in real-world robotics applications is hindered by several challenges, such as unknown agents' preferences and goals. To address these challenges, we show a connection between differential games, optimal control, and energy-based models and demonstrate how existing approaches can be unified under our proposed Energy-based Potential Game formulation. Building upon this formulation, this work introduces a new end-to-end learning application that combines neural networks for game-parameter inference with a differentiable game-theoretic optimization layer, acting as an inductive bias. The experiments using simulated mobile robot pedestrian interactions and real-world automated driving data provide empirical evidence that the game-theoretic layer improves the predictive performance of various neural network backbones.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 47 of its 77 references that are in the map. First posted on arXiv 31 Aug 2023.

Builds on

47 of 77 references.

References · 47

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  4. 2018Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networkscited by 687
  5. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  6. 2021Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Datasetcited by 532
  7. 2020VectorNet: Encoding HD Maps and Agent Dynamics from Vectorized Representationcited by 528
  8. 2021Implicit Behavioral Cloningcited by 442
  9. 2020TNT: Target-driveN Trajectory Predictioncited by 345
  10. 2021How to Train Your Energy-Based Modelscited by 271
  11. 2021MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Predictioncited by 246
  12. 2018Convolutional Social Pooling for Vehicle Trajectory Predictioncited by 221
35 more
  1. 2022Stochastic Trajectory Prediction via Motion Indeterminacy Diffusioncited by 184
  2. 2021DC3: A learning method for optimization with hard constraintscited by 181
  3. 2019PRECOG: PREdiction Conditioned On Goals in Visual Multi-Agent Settingscited by 178
  4. 2016A Theory of Generative ConvNetcited by 174
  5. 2016A Connection between Generative Adversarial Networks, Inverse Reinforcement Learning, and Energy-Based Modelscited by 167
  6. 2020Human Trajectory Forecasting in Crowds: A Deep Learning Perspectivecited by 128
  7. 2020Implicit Latent Variable Model for Scene-Consistent Motion Forecastingcited by 116
  8. 2021Reward (Mis)design for Autonomous Drivingcited by 102
  9. 2021Explainability of deep vision-based autonomous driving systems: Review and challengescited by 80
  10. 2019What the Constant Velocity Model Can Teach Us About Pedestrian Motion Predictioncited by 78
  11. 2022Differentiable Integrated Motion Prediction and Planning with Learnable Cost Function for Autonomous Drivingcited by 71
  12. 2022Theseus: A Library for Differentiable Nonlinear Optimizationcited by 64
  13. 2020DSDNet: Deep Structured self-Driving Networkcited by 61
  14. 2016Cooperative Training of Descriptor and Generator Networkscited by 60
  15. 2022A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Modelcited by 44
  16. 2020Learning Energy-Based Model with Variational Auto-Encoder as Amortized Samplercited by 43
  17. 2022JFP: Joint Future Prediction with Interactive Multi-Agent Modeling for Autonomous Drivingcited by 40
  18. 2019Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Gamescited by 37
  19. 2022DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehiclescited by 36
  20. 2017End-to-End Learning for Structured Prediction Energy Networkscited by 33
  21. 2019Model Based Planning with Energy Based Modelscited by 32
  22. 2021Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutionscited by 22
  23. 2020LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planningcited by 17
  24. 2023Joint Metrics Matter: A Better Standard for Trajectory Forecastingcited by 17
  25. 2021ALGAMES: A Fast Augmented Lagrangian Solver for Constrained Dynamic Gamescited by 16
  26. 2019Energy-Based Continuous Inverse Optimal Controlcited by 14
  27. 2020Learning Game-Theoretic Models of Multiagent Trajectories Using Implicit Layerscited by 13
  28. 2021Inferring Objectives in Continuous Dynamic Games from Noise-Corrupted Partial State Observationscited by 13
  29. 2022Learning to Play Trajectory Games Against Opponents with Unknown Objectivescited by 11
  30. 2020Inference-Based Strategy Alignment for General-Sum Differential Gamescited by 10
  31. 2022Importance is in your attention: agent importance prediction for autonomous drivingcited by 10
  32. 2021Potential iLQR: A Potential-Minimizing Controller for Planning Multi-Agent Interactive Trajectoriescited by 8
  33. 2022Interventional Behavior Prediction: Avoiding Overly Confident Anticipation in Interactive Predictioncited by 8
  34. 2022Differentiable Constrained Imitation Learning for Robot Motion Planning and Controlcited by 7
  35. 2023Distributed Potential iLQR: Scalable Game-Theoretic Trajectory Planning for Multi-Agent Interactionscited by 3

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 3.

4 papers.

  1. 2023Energy-based Potential Games for Joint Motion Forecasting and Controlcited by 9
  2. 2024DiffTORI: Differentiable Trajectory Optimization for Deep Reinforcement and Imitation Learningcited by 5
  3. 2024LoRD: Adapting Differentiable Driving Policies to Distribution Shiftscited by 4
  4. 2024Distributed Stackelberg Strategies in State-based Potential Games for Autonomous Decentralized Learning Manufacturing Systemscited by 1