[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123836-en":3,"doc-seo-123836-105":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":20,"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},123836,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","The Diminishing Returns (DR) Property and Its Applications in Machine Learning","Numerous learning tasks rely on objective functions with a Diminishing Returns (DR) property, where additional input yields progressively smaller marginal gains. This dissertation studies both set functions and continuous functions exhibiting DR, focusing on submodular set functions and continuous DR-submodular functions. Contributions address online and offline maximization: online DR-submodular maximization under budget constraints via primal-dual methods; offline and online strongly DR-submodular maximization with improved convergence and regret; and social/economic settings such as privacy and strategic behavior using differentially private and incentive-compatible algorithms.","©Copyright 2023 Omid Sadeghi  \nThe Diminishing Returns (DR) Property and Its Applications in  \nMachine Learning  \nOmid Sadeghi  \nA dissertation  \nsubmitted in partial fulfillment of the  \nrequirements for the degree of  \nDoctor of Philosophy  \nUniversity of Washington  \n2023  \nReading Committee:  \nMaryam Fazel, Chair  \nJeffrey A. Bilmes  \nKevin Jamieson  \nProgram Authorized to Offer Degree:  \nElectrical and Computer Engineering  \nUniversity of Washington  \nAbstract  \nThe Diminishing Returns (DR) Property and Its Applications in Machine Learning  \nOmid Sadeghi  \nChair of the Supervisory Committee:  \nMaryam Fazel  \nDepartment of Electrical and Computer Engineering  \nNumerous tasks in machine learning involve objective functions that exhibit a Diminishing Returns (DR) property, i.e., the marginal gain of increasing the input gets smaller as the input gets larger. For instance, in document summarization, the goal is to select a small subset of sentences that represent the entirety of the document. As the summary gets larger, the additional benefit of adding a sentence to the summary diminishes. In this dissertation, we focus on the class of set functions and continuous functions that exhibit the DR property. These functions are called submodular set functions and continuous DR-submodular functions respectively. This dissertation presents several contributions to various online and offline maximization problems in machine learning where the utility functions satisfy the DR property, with the main themes organized into three parts: (i) study of online DR-submodular maximization under online budget constraints and designing primal-dual algorithms that not only perform well in terms of the utility, but they also satisfy the online constraints; (ii) characterization of the class of strongly DR-submodular functions and providing techniques for offline and online maximization of these functions that utilize the additional structure to obtain improved convergence rates and regret guarantees respectively; and (iii) study of offline and online submodular set function maximization problems under social and economic considerations (e.g., privacy and strategic behavior) and designing differentially private and incentive-compatible algorithms for these problems.  \nTABLE OF CONTENTS  \nPage  \nList [of Figures ........................................ vi](of Figures ........................................ vi)  \n[Chapter 1: Introduction ................................. 1](Chapter 1: Introduction ................................. 1)  \n[1.1 Outline ....................................... 2](1.1 Outline ....................................... 2)  \n[1.2 Publications ..................................... 3](1.2 Publications ..................................... 3)  \n[Chapter 2: Preliminaries ................................ 5](Chapter 2: Preliminaries ................................ 5)  \n[2.1 Notation ....................................... 5](2.1 Notation ....................................... 5)  \n[2.2 Submodular set functions ............................. 6](2.2 Submodular set functions ............................. 6)  \n[2.3 Continuous DR-submodular functions ...................... 6](2.3 Continuous DR-submodular functions ...................... 6)  \n[2.4 Examples of continuous DR-submodular functions ............... 7](2.4 Examples of continuous DR-submodular functions ............... 7)  \n[Part I: Online Budget-Constrained DR-Submodular Maximization ....... 9](Part I: Online Budget-Constrained DR-Submodular Maximization ....... 9)  \n[Chapter 3: Competitive Algorithms for Online Budget-Constrained DR-Submodular](Chapter 3: Competitive Algorithms for Online Budget-Constrained DR-Submodular)[ ](Chapter 3: Competitive Algorithms for Online Budget-Constrained DR-Submodular)Maximization ................................ 10  \n3.1 Chapter overview .................................. 10  \n3.2 Introduction ..................................... 10  \n3.3 Pro","cbCaivqnCWurCfvr","https://ap.wps.com/l/cbCaivqnCWurCfvr","pdf",8303035,1,277,"English","en",105,"# Chapter 1: Introduction\n## 1.1 Outline\n## 1.2 Publications\n# Chapter 2: Preliminaries\n## 2.1 Notation\n## 2.2 Submodular set functions\n## 2.3 Continuous DR-submodular functions\n## 2.4 Examples of continuous DR-submodular functions\n# Part I: Online Budget-Constrained DR-Submodular Maximization\n## Chapter 3: Competitive Algorithms for Online Budget-Constrained DR-Submodular Maximization\n## Chapter 4: Online DR-Submodular Maximization with Long-Term Adversarial Constraints\n## Chapter 5: Online DR-Submodular Maximization with Long-Term Stochastic Constraints\n## Chapter 6: A Single Recipe for Online DR-Submodular Maximization with Adversarial or Stochastic Constraints\n# Part II: Strongly DR-Submodular Maximization","[{\"question\":\"What does the Diminishing Returns (DR) property mean in machine learning objectives?\",\"answer\":\"It means the marginal gain from increasing the input decreases as the input becomes larger. Many tasks can be modeled so that adding more yields progressively smaller benefit.\"},{\"question\":\"Which function classes does the dissertation study to formalize DR behavior?\",\"answer\":\"It studies DR for both set functions and continuous functions. The corresponding classes are submodular set functions and continuous DR-submodular functions.\"},{\"question\":\"How does the dissertation handle online maximization under constraints?\",\"answer\":\"It develops algorithms for online DR-submodular maximization under budget constraints, including primal-dual approaches. It also studies long-term adversarial and stochastic constraints and analyzes resulting performance.\"}]","The Diminishing Returns (DR) Property and Its Applications in Machine Learning | PDF",1785818820,698,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"the-diminishing-returns-dr-property-and-its-applications-in-machine-learning","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/the-diminishing-returns-dr-property-and-its-applications-in-machine-learning/123836/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What does the Diminishing Returns (DR) property mean in machine learning objectives?","Question",{"text":75,"@type":76},"It means the marginal gain from increasing the input decreases as the input becomes larger. Many tasks can be modeled so that adding more yields progressively smaller benefit.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which function classes does the dissertation study to formalize DR behavior?",{"text":80,"@type":76},"It studies DR for both set functions and continuous functions. The corresponding classes are submodular set functions and continuous DR-submodular functions.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the dissertation handle online maximization under constraints?",{"text":84,"@type":76},"It develops algorithms for online DR-submodular maximization under budget constraints, including primal-dual approaches. 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