Linear Convergent Distributed Nash Equilibrium Seeking With Compression

• 成果类型: Article
• 署名作者: Chen, Xiaomeng; Wu, Yuchi; Yi, Xinlei; Huang, Minyi; Shi, Ling
• 署名单位: Hong Kong University of Science & Technology; Shanghai University; Tongji University; Massachusetts Institute of Technology (MIT); Carleton University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3505812
• 发表日期: 2025
• 页码: 3316-3323
• 关键词: Compressors; games; vectors; Nash equilibrium; CONVERGENCE; Directed graphs; bandwidth; Quantization (signal); Linear matrix inequalities; Finite element analysis; distributed networks; information compression; Nash equilibrium (NE) seeking; Noncooperative games

摘要

Information compression techniques are majorly employed to reduce communication cost over peer-to-peer links. In this article, we investigate distributed Nash equilibrium (NE) seeking problems in a class of noncooperative games over directed graphs with information compression. To improve communication efficiency, a compressed distributed NE seeking (C-DNES) algorithm is proposed to obtain an NE for games, where the differences between decision vectors and their estimates are compressed. The proposed algorithm is compatible with a general class of compressors, including both unbiased and biased compressors. Moreover, our approach only requires the adjacency matrix of the directed graph to be row-stochastic, in contrast to past works that relied on balancedness or specific global network parameters. It is shown that C-DNES not only inherits the advantages of conventional distributed NE algorithms, achieving linear convergence rate for games with restricted strongly monotone mappings, but also saves communication costs in terms of transmitted bits. Finally, numerical simulations illustrate the advantages of C-DNES in saving communication cost by an order of magnitude under different compressors.