In this paper,the author is concerned with the problem of achieving Nash equilibrium in noncooperative games over networks.The author proposes two types of distributed projected gradient dynamics with accelerated conv...In this paper,the author is concerned with the problem of achieving Nash equilibrium in noncooperative games over networks.The author proposes two types of distributed projected gradient dynamics with accelerated convergence rates.The first type is a variant of the commonly-known consensus-based gradient dynamics,where the consensual terms for determining the actions of each player are discarded to accelerate the learning process.The second type is formulated by introducing the Nesterov's accelerated method into the distributed projected gradient dynamics.The author proves convergence of both algorithms with at least linear rates under the common assumption of Lipschitz continuity and strongly monotonicity.Simulation examples are presented to validate the outperformance of the proposed algorithms over the well-known consensus-based approach and augmented game based approach.It is shown that the required number of iterations to reach the Nash equilibrium is greatly reduced in the proposed algorithms.These results could be helpful to address the issue of long convergence time in partial-information Nash equilibrium seeking algorithms.展开更多
Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully...Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.T2322023Hunan Provincial Natural Science Foundation of China under Grant No.2022JJ20018。
文摘In this paper,the author is concerned with the problem of achieving Nash equilibrium in noncooperative games over networks.The author proposes two types of distributed projected gradient dynamics with accelerated convergence rates.The first type is a variant of the commonly-known consensus-based gradient dynamics,where the consensual terms for determining the actions of each player are discarded to accelerate the learning process.The second type is formulated by introducing the Nesterov's accelerated method into the distributed projected gradient dynamics.The author proves convergence of both algorithms with at least linear rates under the common assumption of Lipschitz continuity and strongly monotonicity.Simulation examples are presented to validate the outperformance of the proposed algorithms over the well-known consensus-based approach and augmented game based approach.It is shown that the required number of iterations to reach the Nash equilibrium is greatly reduced in the proposed algorithms.These results could be helpful to address the issue of long convergence time in partial-information Nash equilibrium seeking algorithms.
基金supported by the National Natural Science Foundation of China(Nos.11661141019 and 61621003)the National Ten Thousand Talent Program for Young Topnotch Talents+1 种基金Chinese Academy Science(CAS)Frontier Science Research Key Project for Top Young Scientist(No.QYZDB-SSW-SYS008)the Key Laboratory of Random Complex Structures and Data Science,CAS(No.2008DP173182).
文摘Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.
