The broad goal of the research surveyed in this article is to develop methods for understanding the aggregate behavior of interconnected dynamical systems,as found in mathematical physics,neuroscience,economics,power ...The broad goal of the research surveyed in this article is to develop methods for understanding the aggregate behavior of interconnected dynamical systems,as found in mathematical physics,neuroscience,economics,power systems and neural networks.Questions concern prediction of emergent(often unanticipated)phenomena,methods to formulate distributed control schemes to influence this behavior,and these topics prompt many other questions in the domain of learning.The area of mean field games,pioneered by Peter Caines,are well suited to addressing these topics.The approach is surveyed in the present paper within the context of controlled coupled oscillators.展开更多
Several decades ago,Profs.Sean Meyn and Lei Guo were postdoctoral fellows at ANU,where they shared interest in recursive algorithms.It seems fitting to celebrate Lei Guo’s 60 th birthday with a review of the ODE Meth...Several decades ago,Profs.Sean Meyn and Lei Guo were postdoctoral fellows at ANU,where they shared interest in recursive algorithms.It seems fitting to celebrate Lei Guo’s 60 th birthday with a review of the ODE Method and its recent evolution,with focus on the following themes:The method has been regarded as a technique for algorithm analysis.It is argued that this viewpoint is backwards:The original stochastic approximation method was surely motivated by an ODE,and tools for analysis came much later(based on establishing robustness of Euler approximations).The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time,following by careful approximation to obtain a practical recursive algorithm.While these methods are usually presented in a stochastic setting,this is not a prerequisite.In fact,recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo.Subject to conditions,the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert.The conditions are not universal,but theory suggests alternatives to achieve acceleration.The theory is illustrated with applications to gradient-free optimization,and policy gradient algorithms for reinforcement learning.展开更多
基金supported by AFOSR under Grant No.FA9550-23-1-0060NSF under Grant Nos.2336137(Mehta)and 2306023(Meyn).
文摘The broad goal of the research surveyed in this article is to develop methods for understanding the aggregate behavior of interconnected dynamical systems,as found in mathematical physics,neuroscience,economics,power systems and neural networks.Questions concern prediction of emergent(often unanticipated)phenomena,methods to formulate distributed control schemes to influence this behavior,and these topics prompt many other questions in the domain of learning.The area of mean field games,pioneered by Peter Caines,are well suited to addressing these topics.The approach is surveyed in the present paper within the context of controlled coupled oscillators.
基金ARO W911NF1810334NSF under EPCN 1935389the National Renewable Energy Laboratory(NREL)。
文摘Several decades ago,Profs.Sean Meyn and Lei Guo were postdoctoral fellows at ANU,where they shared interest in recursive algorithms.It seems fitting to celebrate Lei Guo’s 60 th birthday with a review of the ODE Method and its recent evolution,with focus on the following themes:The method has been regarded as a technique for algorithm analysis.It is argued that this viewpoint is backwards:The original stochastic approximation method was surely motivated by an ODE,and tools for analysis came much later(based on establishing robustness of Euler approximations).The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time,following by careful approximation to obtain a practical recursive algorithm.While these methods are usually presented in a stochastic setting,this is not a prerequisite.In fact,recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo.Subject to conditions,the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert.The conditions are not universal,but theory suggests alternatives to achieve acceleration.The theory is illustrated with applications to gradient-free optimization,and policy gradient algorithms for reinforcement learning.
