Linear-Quadratic Gaussian Games with Distributed Sparse Estimation

TL;DR

This paper introduces a distributed sparse estimation method for linear-quadratic Gaussian games, reducing communication costs while maintaining effective strategic decision-making in multi-agent systems.

Contribution

It proposes a novel group lasso-based estimator for sparse interagent observations in Gaussian games, with theoretical guarantees and practical simulation validation.

Findings

Significant reduction in communication resources.

Minimal impact on equilibrium trajectories.

Estimator guarantees for estimation quality.

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.