We consider a recent innovative theory by Chastain et al. on the role of sex in evolution [PNAS'14]. In short, the theory suggests that the evolutionary process of gene recombination implements the celebrated multiplicative weights updates algorithm (MWUA). They prove that the population dynamics induced by sexual reproduction can be precisely modeled by genes that use MWUA as their learning strategy in a particular coordination game. The result holds in the environments of \emph{weak selection}, under the assumption that the population frequencies remain a product distribution.
We revisit the theory, eliminating both the requirement of weak selection and any assumption on the distribution of the population. Removing the assumption of product distributions is crucial, since as we show, this assumption is inconsistent with the population dynamics. We show that the marginal allele distributions induced by the population dynamics precisely match the marginals induced by a multiplicative weights update algorithm in this general setting, thereby affirming and substantially generalizing these earlier results.
We further revise the implications for convergence and utility or fitness guarantees in coordination games. In contrast to the claim of Chastain et al.[PNAS'14], we conclude that the sexual evolutionary dynamics does not entail any property of the population distribution, beyond those already implied by convergence.
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）
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）
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）
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）
Learning in Position-Aware Multinomial Logit Bandits: From Multiplicative to General Position Effects
Leonard N. Stern School of Business, New York University（纽约大学勒纳商学院）；Qiuzhen College, Tsinghua University（清华大学齐臻学院）；Department of Management Science, School of Management, Fudan University（复旦大学管理学院管理科学系）；Yau Mathematical Sciences Center & Department of Mathematical Sciences, Tsinghua University（清华大学尤数学科学中心及数学科学系）
Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning
Department of Mathematics, Imperial College London（帝国理工学院数学系）；Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）
