# Auto-Encoding Bayesian Inverse Games

arXiv: https://arxiv.org/abs/2402.08902 · HTML: https://mlsanity.com/paper/2402.08902/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [PixelVAE: A Latent Variable Model for Natural Images](https://mlsanity.com/paper/1611.05013/) (2016)
- [Computational Rationalization: The Inverse Equilibrium Problem](https://mlsanity.com/paper/1308.3506/) (2013)
- [Stochastic Dynamic Games in Belief Space](https://mlsanity.com/paper/1909.06963/) (2019)
- [Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions](https://mlsanity.com/paper/2110.01027/) (2021)
- [A Real-Time Game Theoretic Planner for Autonomous Two-Player Drone Racing](https://mlsanity.com/paper/1801.02302/) (2018)
- [LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planning](https://mlsanity.com/paper/2011.08152/) (2020)
- [ALGAMES: A Fast Augmented Lagrangian Solver for Constrained Dynamic Games](https://mlsanity.com/paper/2104.08452/) (2021)
- [Learning Game-Theoretic Models of Multiagent Trajectories Using Implicit Layers](https://mlsanity.com/paper/2008.07303/) (2020)
- [Contingency Games for Multi-Agent Interaction](https://mlsanity.com/paper/2304.05483/) (2023)
- [Learning to Play Trajectory Games Against Opponents with Unknown Objectives](https://mlsanity.com/paper/2211.13779/) (2022)
- [Active Uncertainty Reduction for Human-Robot Interaction: An Implicit Dual Control Approach](https://mlsanity.com/paper/2202.07720/) (2022)
- [Energy-based Potential Games for Joint Motion Forecasting and Control](https://mlsanity.com/paper/2312.01811/) (2023)
- [The Computation of Approximate Generalized Feedback Nash Equilibria](https://mlsanity.com/paper/2101.02900/) (2021)
- [Cost Inference for Feedback Dynamic Games from Noisy Partial State Observations and Incomplete Trajectories](https://mlsanity.com/paper/2301.01398/) (2023)
- [Online and Offline Learning of Player Objectives from Partial Observations in Dynamic Games](https://mlsanity.com/paper/2302.01999/) (2023)
- [Learning Rationality in Potential Games](https://mlsanity.com/paper/2303.11188/) (2023)

## Built on by (most cited first, 3 of 3)

- [Recent Advances in Multi-Agent Human Trajectory Prediction: A Comprehensive Review](https://mlsanity.com/paper/2506.14831/) (2025)
- [Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions](https://mlsanity.com/paper/2508.19945/) (2025)
- [Generalized Information Gathering Under Dynamics Uncertainty](https://mlsanity.com/paper/2601.21988/) (2026)

## Abstract (arXiv)

When multiple agents interact in a common environment, each agent's actions impact others' future decisions, and noncooperative dynamic games naturally capture this coupling. In interactive motion planning, however, agents typically do not have access to a complete model of the game, e.g., due to unknown objectives of other players. Therefore, we consider the inverse game problem, in which some properties of the game are unknown a priori and must be inferred from observations. Existing maximum likelihood estimation (MLE) approaches to solve inverse games provide only point estimates of unknown parameters without quantifying uncertainty, and perform poorly when many parameter values explain the observed behavior. To address these limitations, we take a Bayesian perspective and construct posterior distributions of game parameters. To render inference tractable, we employ a variational autoencoder (VAE) with an embedded differentiable game solver. This structured VAE can be trained from an unlabeled dataset of observed interactions, naturally handles continuous, multi-modal distributions, and supports efficient sampling from the inferred posteriors without computing game solutions at runtime. Extensive evaluations in simulated driving scenarios demonstrate that the proposed approach successfully learns the prior and posterior game parameter distributions, provides more accurate objective estimates than MLE baselines, and facilitates safer and more efficient game-theoretic motion planning.