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First-Order algorithms for Nonlinear Generalized Nash Equilibrium Problems

JOURNAL OF MACHINE LEARNING RESEARCH 2023年第1期24卷 1-46页

作者： Jordan, Michael I. Lin, Tianyi Zampetakis, Manolis Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA

We consider the problem of computing an equilibrium in a class of nonlinear generalized Nash equilibrium problems (NGNEPs) in which the strategy sets for each player are de -fined by equality and inequality constraints that may depend on the choices of rival players. While the asymptotic global convergence and local convergence rates of algorithms to solve this problem have been extensively investigated, the analysis of nonasymptotic iteration complexity is still in its infancy. This paper presents two first-order algorithms- based on the quadratic penalty method (QPM) and augmented Lagrangian method (ALM), respectively-with an accelerated mirror-prox algorithm as the solver in each inner loop. We establish a global convergence guarantee for solving monotone and strongly monotone NGNEPs and provide nonasymptotic complexity bounds expressed in terms of the number of gradient evaluations. Experimental results demonstrate the efficiency of our algorithms in practice.

关键词： Nonlinear generalized Nash equilibrium problems monotonicity quadratic penalty method augmented Lagrangian method accelerated mirror-prox algorithm

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First-order algorithms for nonlinear generalized Nash equilibrium problems

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 1483-1528页

作者： Michael I. Jordan Tianyi Lin Manolis Zampetakis Department of Electrical Engineering and Computer Science and Department of Statistics University of California Berkeley Berkeley CA Department of Electrical Engineering and Computer Science University of California Berkeley Berkeley CA

We consider the problem of computing an equilibrium in a class of nonlinear generalized Nash equilibrium problems (NGNEPs) in which the strategy sets for each player are defined by equality and inequality constraints that may depend on the choices of rival players. While the asymptotic global convergence and local convergence rates of algorithms to solve this problem have been extensively investigated, the analysis of nonasymptotic iteration complexity is still in its infancy. This paper presents two first-order algorithms-- based on the quadratic penalty method (QPM) and augmented Lagrangian method (ALM), respectively--with an accelerated mirror-prox algorithm as the solver in each inner loop. We establish a global convergence guarantee for solving monotone and strongly monotone NGNEPs and provide nonasymptotic complexity bounds expressed in terms of the number of gradient evaluations. Experimental results demonstrate the efficiency of our algorithms in practice.

关键词： nonlinear generalized Nash equilibrium problems monotonicity quadratic penalty method augmented Lagrangian method accelerated mirror-prox algorithm

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