Distributed GNE Seeking Under Partial-Decision Information Over Networks via a Doubly-Augmented Operator Splitting Approach

• Published in: IEEE transactions on automatic control Vol. 65; no. 4; pp. 1584 - 1597
• Main Author: Pavel, Lacra
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Convergence; Couplings; Eigenvalues and eigenfunctions; Game theory; Games; Generalized Nash equilibrium (GNE); Heuristic algorithms; Iterative methods; Nash equilibrium; Operators; Peer-to-peer computing; variational inequality (VI)
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2019.2922953

We consider distributed computation of generalized Nash equilibrium (GNE) over networks, in games with shared coupling constraints. Existing methods require that each player has full access to opponents' decisions. In this paper, we assume that players have only partial-decision information, and can communicate with their neighbors over an arbitrary undirected graph. We recast the problem as that of finding a zero of a sum of monotone operators through primal-dual analysis. To distribute the problem, we doubly augment variables, so that each player has local decision estimates and local copies of Lagrangian multipliers. We introduce a single-layer algorithm, fully distributed with respect to both primal and dual variables. We show its convergence to a variational GNE with fixed step sizes, by reformulating it as a forward-backward iteration for a pair of doubly-augmented monotone operators.