We present multiplicative updates for solving hard and soft margin support vector machines (SVM) with non-negative kernels. They follow as a natural extension of the updates for non-negative matrix factorization. No additional param- eter setting, such as choosing learning, rate is required. Ex- periments demonstrate rapid convergence to good classifiers. We analyze the rates of asymptotic convergence of the up- dates and establish tight bounds. We test the performance on several datasets using various non-negative kernels and report equivalent generalization errors to that of a standard SVM.
Multiplicative updates for symmetric-cone factorizations
National University of Singapore（新加坡国立大学）；Institute of High Performance Computing, Agency for Science, Technology and Research（新加坡科技研究局高性能计算研究院）；Singapore University of Technology and Design（新加坡科技设计大学）
A Non-commutative Extension of Lee-Seung's Algorithm for Positive Semidefinite Factorizations
National University of Singapore（新加坡国立大学）；Institute of High Performance Computing, Agency for Science, Technology and Research（新加坡科技研究局高性能计算研究所）；Singapore University of Technology and Design（新加坡科技设计大学）
Consensus Multiplicative Weights Update: Learning to Learn using Projector-based Game Signatures
J.P. Morgan AI Research（摩根大通人工智能研究院）；University of Liverpool（利物浦大学）
Cheung和Piliouras（2020）最近表明，乘法权重更新方法的两个变体- OMWU和MWU -根据游戏是零和还是合作而显示相反的收敛特性。受这项工作和最近的文献学习优化单功能的启发，我们引入了一个新的框架，学习最后一次收敛到纳什均衡的游戏，其中更新规则的系数（学习率）沿轨迹学习的强化学习策略，是有条件的游戏的性质：\textit{the game signature}。我们构造后者使用一个新的分解成8个组件对应于交换投影算子的两个玩家的游戏，推广和统一最近的游戏概念在文献中研究。我们比较了各种更新规则的性能时，他们的系数学习，并表明RL政策是能够利用游戏签名在广泛的游戏类型。在这样做时，我们引入CMWU，一个新的算法，扩展共识优化的约束情况下，具有局部收敛保证零和双矩阵游戏，并显示它享有竞争力的性能与常系数的零和游戏和整个频谱的游戏时，其系数的学习。
Langevin Multiplicative Weights Update with Applications in Polynomial Portfolio Management
School of Information Management & Engineering, Shanghai University of Finance and Economics（上海财经大学信息管理与工程学院）；College of Business, Shanghai University of Finance and Economics（上海财经大学商学院）
Block Majorization Minimization with Extrapolation and Application to $β$-NMF
Acapela Group（Acapela集团）；Institute of data sciences（数据科学研究所）；Faculty of Engineering（工程学院）；University of Mons（蒙斯大学）；Department of Mathematics and Operational Research（数学与运筹学系）
Elastic-Net Multiple Kernel Learning: Combining Multiple Data Sources for Prediction
Centre for Artificial Intelligence, Department of Computer Science, University College London, UK（人工智能中心、计算机科学系、伦敦大学学院、英国）；Hawkes Institute, University College London, UK（霍克斯研究所、伦敦大学学院、英国）；Department of Computer Science, University College London, UK（计算机科学系、伦敦大学学院、英国）；GIGA - CRC Human Imaging, University of Liège, Belgium（GIGA- CRC 人类成像、列日大学、比利时）
Fast and Scalable Adversarial Training of Kernel SVM via Doubly Stochastic Gradients
Nanjing University of Information Science & Technology（南京信息工程大学）；University of Pittsburgh（匹兹堡大学）；JD Finance America Corporation（京东金融美国公司）；MBZUAI（穆罕默德·本·扎耶德人工智能大学）
Multiplicative learning from observation-prediction ratios
Department of Physics Education, Seoul National University（首尔国立大学物理教育系）；Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases（糖尿病与消化系统疾病国家研究所生物建模实验室）；Center for Theoretical Physics and Artificial Intelligence Institute, Seoul National University（首尔国立大学理论物理与人工智能研究所）；School of Computational Sciences, Korea Institute for Advanced Study（韩国高级研究院计算科学系）
Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications
School of Engineering and Applied Sciences, Harvard University, MA, USA（哈佛大学工程与应用科学学院）；Center on Frontiers of Computing Studies and School of Computer Science, Peking University, Beijing, China（前沿计算研究中心和北京大学计算机科学学院）；Department of Statistics and Data Science, Carnegie Mellon University, PA, USA（统计与数据科学系，卡内基梅隆大学）
Robust Non-negative Proximal Gradient Algorithm for Inverse Problems
Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；Beihang University（北京航空航天大学）；Harbin Institute of Technology（哈尔滨工业大学）；City University of Hong Kong（香港城市大学）
