[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118352-en":3,"doc-seo-118352-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118352,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Integration of Control and Dynamical Systems Perspectives to Machine Learning","Integration of machine learning with control and dynamical systems addresses the need for reliable AI behavior over sequential data in robotics and language processing. The dissertation synthesizes research at the intersection of learning and dynamical modeling, proposing techniques that transfer domain concepts into unified learning-and-control paradigms. Contributions include learning algorithms with control-theoretic guarantees via limited-duration safety, a model-based RL method using a control-theoretic oracle, Koopman-based formulations for nonlinear behavior design, path-based exploration beyond Bellman recursion, and theoretical tools to mitigate loss of dynamic structure from measure concentration. It concludes with a perspective linking learning algorithms as dynamical systems and outlining future research.","©Copyright 2024 Motoya Ohnishi  \nIntegration of Control and Dynamical Systems Perspectives to  \nMachine Learning  \nMotoya Ohnishi  \nA dissertation  \nsubmitted in partial fulfillment of the  \nrequirements for the degree of  \nDoctor of Philosophy  \nUniversity of Washington  \n2024  \nReading Committee:  \nSham Kakade, Chair  \nEmanuel Todorov, Chair  \nFabio Ramos  \nProgram Authorized to Offer Degree:  \nComputer Science & Engineering  \nUniversity of Washington  \nAbstract  \nIntegration of Control and Dynamical Systems Perspectives to Machine Learning  \nMotoya Ohnishi  \nCo-Chairs of the Supervisory Committee:  \nSham Kakade  \nComputer Science & Engineering  \nEmanuel Todorov  \nComputer Science & Engineering  \nWith the increasing demands on artificial intelligence technology operating over sequential data, represented by robotics and language processing, there has been a surge of interest in interdisciplinary research spanning machine learning – a data-driven approach based on statistics – and control or dynamical systems theory, which deals with dynamic environments. Because those streams of studies have evolved in a relatively separate manner under different settings and formulations, their integration becomes an intricate task, requiring afresh look at the existing approach. This thesis primarily revolves around a discussion of research endeavors in the intersection of machine learning and dynamical systems to exploit the best of both worlds, and proposes some of the novel techniques and paradigms made possible by bringing the unique perspectives and concepts from these domains creatively. I initially provide a succinct overview of the state of the art in the related domains followed by my contributions to the fields. First of all, this thesis begins with the work that synthesizes control tools in a learning system to devise algorithms with control theoretic guarantees. In this process, a novel control concept, limited-duration safety, is proposed with discussionson its application within the context of transfer learning. Secondly, a novel model-based reinforcement learning (RL) algorithm is presented, leveraging a recent control theoretic tool  \nas an oracle embedded in the algorithm to provably ensure learning efficiency. With a novel problem formulation with the Koopman operator, which is cast as a generalization of pole assignments to nonlinear decision making, a diverse array of dynamic behaviors are realized. Thirdly, as an additional highlight of exploration, I present the successful extension of RL beyond its conventional reliance on the Bellman equation, encompassing dynamic programming across entire paths. The new framework grounded in theoretical advancements of path signatures has proven beneficial in addressing challenges related to path following. On the other hand, merging machine learning, rooted in statistics, and dynamical systems raises several challenges. In particular, fourthly, this thesis discusses a specific challenge of loss of dynamic structure information that might be caused by concentrations of measures, which is overcome by carefully adopting the asymptotic results of exponential sums. Lastly, a machine learning algorithm itself can be seen as a dynamical system, and this perspective has theoretical and practical potential for handling complex machine learning domains. Especially for a deep RL algorithm, the constructive approach is taken to analyze, in a retroductive manner, the phenomena and performance separations observed in the systems of interest. This thesis is also intended to open a novel direction of further research emerging out of amalgamations of learning algorithms and dynamical systems perspectives, and is concluded with a remark for the potential future work.  \nTABLE OF CONTENTS  \nPage  \nNomenclature ........................................ 1  \nChapter 1: Introduction ................................ 3  \n1.1 Motivation ..................................... 3  \n1.2 Thesis statement and summa","cbCaicyHoa0DgRHa","https://ap.wps.com/l/cbCaicyHoa0DgRHa","pdf",20619897,1,306,"English","en",105,"# Nomenclature\n# Chapter 1: Introduction\n## Motivation\n## Thesis statement and summary\n## Summary of contributions\n# Chapter 2: Background\n## Reviews of mathematical concepts\n## Related work\n# Chapter 3: Control theoretic guarantees for machine learning algorithm\n## Introduction\n## Problem setups\n## Constraint learning for control tasks\n## Applications\n## Chapter summary and discussion\n# Chapter 4: Problem formulations through the lens of dynamical systems\n## Introduction\n## Model-based RL with an optimal control oracle embedded\n## Reframing and generalizing a unique control problem as ML\n## Chapter summary and discussion\n# Chapter 5: Trajectory-based optimization for control and learning tasks\n## Introduction\n## Problem setups\n## Signature control\n## Signature MPC\n## Experimental results\n## Chapter summary and discussion\n# Chapter 6: Algorithm design at the intersection of statistical ML and dynamical systems\n## Introduction\n## Problem setups\n## Algorithms and theory\n## Simulated experiments\n## Applications to bandit problems\n## Chapter summary and discussion","[{\"question\":\"What is the main goal of the dissertation?\",\"answer\":\"The dissertation aims to integrate machine learning with control and dynamical systems perspectives, addressing how these fields can be combined to develop new learning techniques and paradigms for sequential-data settings.\"},{\"question\":\"How does the thesis obtain control-theoretic guarantees in learning?\",\"answer\":\"It presents work that synthesizes control tools within learning systems, including a proposed concept called limited-duration safety and discussions of its use in transfer learning.\"},{\"question\":\"What reinforcement learning extensions are introduced beyond conventional approaches?\",\"answer\":\"The thesis presents a model-based RL algorithm using a control-theoretic oracle, formulates learning through the Koopman-operator lens, and extends exploration beyond reliance on the Bellman equation using path-based dynamic programming grounded in path signatures.\"}]","Integration of Control and Dynamical Systems Perspectives to Machine Learning | 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is the main goal of the dissertation?","Question",{"text":75,"@type":76},"The dissertation aims to integrate machine learning with control and dynamical systems perspectives, addressing how these fields can be combined to develop new learning techniques and paradigms for sequential-data settings.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the thesis obtain control-theoretic guarantees in learning?",{"text":80,"@type":76},"It presents work that synthesizes control tools within learning systems, including a proposed concept called limited-duration safety and discussions of its use in transfer learning.",{"name":82,"@type":73,"acceptedAnswer":83},"What reinforcement learning extensions are introduced beyond conventional approaches?",{"text":84,"@type":76},"The thesis presents a model-based RL algorithm using a control-theoretic oracle, formulates learning through the Koopman-operator lens, and extends exploration beyond reliance on the Bellman equation using path-based 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