Learning in Inverse Games: Tractable Training with Probabilistic Guarantees
Abstract
Inverse game theory seeks to learn agents' unknown objectives from observed equilibrium behavior. Existing residual-based approaches can lead to non-convex problems and need not ensure strong monotonicity of the learned game, limiting reliable equilibrium prediction. We develop a tractable convex framework for learning static and dynamic non-cooperative games using first-order and Nikaido-Isoda (NI) loss. Specialized operator parameterizations, including a Helmholtz--Hodge decomposition in a reproducing kernel Hilbert space (RKHS), enforce strong monotonicity for quadratic, nonparametric, non-quadratic, and linear-quadratic dynamic games. We establish finite-sample out-of-sample prediction guarantees, using Rademacher complexity to match existing bounds for the non-quadratic setting. For noisy sequential data, we develop a robust receding-horizon learning scheme whose adaptive regularization admits a maximum a posteriori (MAP) interpretation and is computed using randomized trace estimation. Numerical experiments, including a stylized autonomous-vehicle collision-avoidance application, demonstrate predictive accuracy and robustness to measurement noise.
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BibTeX
@misc{mallick2026learning,
title = {{Learning in Inverse Games: Tractable Training with Probabilistic Guarantees}},
author = {Arghya Mallick and Reza Rahimi Baghbadorani and Peyman Mohajerin Esfahani and Sergio Grammatico},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03481},
eprint = {2610.03481},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03481},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Learning in Inverse Games: Tractable Training with Probabilistic Guarantees
AU - Arghya Mallick
AU - Reza Rahimi Baghbadorani
AU - Peyman Mohajerin Esfahani
AU - Sergio Grammatico
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03481
UR - https://arxiv.org/abs/2610.03481
AB - Inverse game theory seeks to learn agents' unknown objectives from observed equilibrium behavior. Existing residual-based approaches can lead to non-convex problems and need not ensure strong monotonicity of the learned game, limiting reliable equilibrium prediction. We develop a tractable convex framework for learning static and dynamic non-cooperative games using first-order and Nikaido-Isoda (NI) loss. Specialized operator parameterizations, including a Helmholtz--Hodge decomposition in a reproducing kernel Hilbert space (RKHS), enforce strong monotonicity for quadratic, nonparametric, non-quadratic, and linear-quadratic dynamic games. We establish finite-sample out-of-sample prediction guarantees, using Rademacher complexity to match existing bounds for the non-quadratic setting. For noisy sequential data, we develop a robust receding-horizon learning scheme whose adaptive regularization admits a maximum a posteriori (MAP) interpretation and is computed using randomized trace estimation. Numerical experiments, including a stylized autonomous-vehicle collision-avoidance application, demonstrate predictive accuracy and robustness to measurement noise.
ER -