A doubly-augmented operator splitting approach for distributed GNE seeking over networks
Lacra Pavel · 2018
We consider distributed generalized Nash equilibrium (GNE) seeking over networks, in games with shared affine constraints. Existing methods require that each player has full access to opponents' decisions. Here we assume that players have only partial-decision information, and can communicate with their neighbours over an arbitrary undirected graph. We recast the problem as one of zero finding for a sum of monotone operators through primal-dual analysis. To distribute the problem, we doubly augment variables: each player has local decision estimates and local copies of Lagrangian multipliers. We propose a single-layer algorithm, fully distributed with respect to both primal and dual variables, based on a forward-backward splitting for doubly-augmented monotone operators. We show its convergence with fixed step-sizes, under cocoercivity of the extended pseudo-gradient.