Two-timescale recurrent neural networks for distributed minimax optimization

Zicong Xia; Yang Liu; Jiasen Wang; Jun Wang

doi:10.1016/j.neunet.2023.06.003

Two-timescale recurrent neural networks for distributed minimax optimization

Neural Netw. 2023 Aug:165:527-539. doi: 10.1016/j.neunet.2023.06.003. Epub 2023 Jun 9.

Authors

Zicong Xia¹, Yang Liu², Jiasen Wang³, Jun Wang⁴

Affiliations

¹ School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China.
² Key Laboratory of Intelligent Education Technology and Application of Zhejiang Province, Zhejiang Normal University, Jinhua 321004, China; School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China. Electronic address: [email protected].
³ Future Network Research Center, Purple Mountain Laboratories, Nanjing 211111, China.
⁴ Department of Computer Science and School of Data Science, City University of Hong Kong, Hong Kong. Electronic address: [email protected].

PMID: 37348433
DOI: 10.1016/j.neunet.2023.06.003

Abstract

In this paper, we present two-timescale neurodynamic optimization approaches to distributed minimax optimization. We propose four multilayer recurrent neural networks for solving four different types of generally nonlinear convex-concave minimax problems subject to linear equality and nonlinear inequality constraints. We derive sufficient conditions to guarantee the stability and optimality of the neural networks. We demonstrate the viability and efficiency of the proposed neural networks in two specific paradigms for Nash-equilibrium seeking in a zero-sum game and distributed constrained nonlinear optimization.

Keywords: Distributed optimization; Minimax optimization; Neurodynamic optimization; Recurrent neural networks.

MeSH terms

Algorithms*
Computer Simulation
Neural Networks, Computer*