Approximate Feedback Nash Equilibria With Sparse Inter-agent Dependencies

Abstract

Feedback Nash equilibrium strategies in multi-agent dynamic games require availability of all players' state information to compute control actions. However, in real-world scenarios, sensing and communication limitations between agents make full state feedback expensive or impractical, and such strategies can become fragile when state information from other agents is inaccurate. To this end, we propose a regularized dynamic programming approach for finding sparse feedback policies that selectively depend on the states of a subset of agents in dynamic games. The proposed approach solves convex adaptive group Lasso problems to compute sparse policies approximating Nash equilibrium solutions. We prove the regularized solutions' asymptotic convergence to a neighborhood of Nash equilibrium policies in linear-quadratic (LQ) games. Further, we extend the proposed approach to general non-LQ games via an iterative algorithm. Simulation results in multi-robot interaction scenarios show that the

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