Linear-Quadratic Gaussian Games with Distributed Sparse Estimation
Abstract
Linear-quadratic Gaussian games provide a framework for modeling strategic interactions in multi-agent systems, where agents must estimate system states from noisy observations while also making decisions to optimize a quadratic cost. However, these formulations usually require agents to utilize the full set of available observations when forming their state estimates, which can be unrealistic in large-scale or resource-constrained settings. In this paper, we consider linear-quadratic Gaussian games with sparse interagent observations. To enforce sparsity in the estimation stage, we design a distributed estimator that balances estimation effectiveness with interagent measurement sparsity via a group lasso problem, while agents implement feedback Nash strategies based on their state estimates. We provide sufficient conditions under which the sparse estimator is guaranteed to trigger a corrective reset to the optimal estimation gain, ensuring that estimation quality does not degrade beyond a level determined by the regularization parameters. Simulations on a formation game show that the proposed approach yields a significant reduction in communication resources consumed while only minimally affecting the nominal equilibrium trajectories.
Cite
@article{arxiv.2603.17202,
title = {Linear-Quadratic Gaussian Games with Distributed Sparse Estimation},
author = {Tianyu Qiu and Filippos Fotiadis and Xinjie Liu and Christian Ellis and Jesse Milzman and Wesley Suttle and Ufuk Topcu and David Fridovich-Keil},
journal= {arXiv preprint arXiv:2603.17202},
year = {2026}
}