Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Linear-Quadratic Gaussian Games with Distributed Sparse Estimation

Tianyu Qiu, Filippos Fotiadis, Xinjie Liu, Christian Ellis, Jesse Milzman, Wesley Suttle, Ufuk Topcu, David Fridovich-Keil

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.

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.
Paper Structure (15 sections, 2 theorems, 31 equations, 4 figures, 1 algorithm)

This paper contains 15 sections, 2 theorems, 31 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Linear-Quadratic Gaussian Games with Individual Observations
  3. Linear-Quadratic Gaussian Games
  4. Individual Observation Model
  5. Control, Estimation, and Information Patterns
  6. Distributed Sparse Estimation Gain Design
  7. Propagation of Joint Estimation Error and Covariance
  8. Distributed Optimal Estimation Design
  9. Sparse Estimation via Group Lasso Optimization
  10. Game-Theoretic Control-Adaptive Regularization
  11. Covariance-Sparsity Trade-Off
  12. Numerical Simulations
  13. Simulation Setup
  14. Result Analysis
  15. Conclusions and Future Work

Key Result

Proposition 1

Problem eqn:lasso_sparse_estimation is equivalent to a convex conic program with quadratic cost.

Figures (4)

  • Figure 1: Feedback LQG game play with distributed sparse estimation in a three-robot formation game.
  • Figure 2: The sensor usage and individual estimation covariance norm evolution of each robot (Row 1: R1, Row 2: R2, we omit R3 as it is symmetric to R2) in the three-robot formation game under constant regularization levels (a) $\lambda_t^i=50$, (b) $\lambda_t^i=1000$ and (c) game-theoretic control-adaptive $\lambda_t^i$.
  • Figure 3: Game-theoretic control-adaptive regularization with respect to feedback Nash control gain $\Gamma_t^i[j]$ in \ref{['eqn:adaptive_lambda']} for a three-robot formation game.
  • Figure 4: Trajectory performance for the formation game with regularization levels (a) $\lambda_t^i=0$, (b) $\lambda_t^i=50$, (c) $\lambda_t^i=1000$, and (d) control-adaptive $\lambda_t^i$.

Theorems & Definitions (5)

  • Remark 1
  • Proposition 1
  • proof
  • Theorem 1
  • proof