Linear Last-Iterate Convergence for Continuous Games with Coupled Inequality Constraints

TL;DR

This paper introduces a decentralized primal-dual algorithm for continuous games with coupled constraints, achieving the first linear convergence for the last-iterate in GNE seeking under partial information.

Contribution

It proposes the first linearly convergent GNE seeking algorithm for coupled affine inequality constraints in a decentralized setting.

Findings

Algorithm converges linearly for the last-iterate.

Effective in partial-decision information scenarios.

Numerical results validate theoretical convergence.

Abstract

In this paper, the generalized Nash equilibrium (GNE) seeking problem for continuous games with coupled affine inequality constraints is investigated in a partial-decision information scenario, where each player can only access its neighbors' information through local communication although its cost function possibly depends on all other players' strategies. To this end, a novel decentralized primal-dual algorithm based on consensus and dual diffusion methods is devised for seeking the variational GNE of the studied games. This paper also provides theoretical analysis to show that the designed algorithm converges linearly for the last-iterate, which, to our best knowledge, is the first to propose a linearly convergent GNE seeking algorithm under coupled affine inequality constraints. Finally, a numerical example is presented to demonstrate the effectiveness of the obtained theoretical results.