[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-268247-105":59,"doc-detail-268247-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","bandit-algorithms","Bandit Algorithms","","Bandit Algorithms presents a rigorous, probabilistic framework for sequential decision-making under uncertainty. It develops foundational tools from probability theory, stochastic processes, and concentration of measure, then analyzes stochastic bandits through explore-then-commit and optimism-based UCB methods. The book extends to adversarial settings with algorithms such as Exp3 and Exp3-IX, establishes lower bounds using information-theoretic techniques, and further treats contextual and linear bandits. It culminates in adversarial linear bandits via convex analysis.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/bandit-algorithms/268247/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/bandit-algorithms/268247.png","ImageObject",300,407,{"name":92,"@type":93},"Miles","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What core concepts does the book cover for bandit problems?","Question",{"text":113,"@type":114},"The book builds on probability spaces, conditional probability, independence, expectation, stochastic processes, Markov chains, martingales, stopping times, and concentration of measure. These tools support regret analysis across multiple bandit settings.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the book treat stochastic bandits with finitely many arms?",{"text":118,"@type":114},"It analyzes algorithms such as Explore-Then-Commit and Upper Confidence Bound (UCB) variants, including asymptotic and minimax optimality perspectives and specialized analyses like Bernoulli noise. It also decomposes regret to support the theoretical results.",{"name":120,"@type":111,"acceptedAnswer":121},"How are adversarial bandits and lower bounds handled?",{"text":122,"@type":114},"Adversarial bandits are addressed with algorithms like Exp3 and Exp3-IX under adversarial bandit environments and importance-weighted estimators. Lower bounds are derived using information-theoretic foundations such as entropy and relative entropy, then extended to minimax, instance-dependent, and high-probability forms.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},268247,1789429623,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Bandit Algorithms  \nTor Lattimore and Csaba Szepesv ri  \nThis is the (free) online edition. The content is the same as the print edition, published by Cambridge University Press, except that minor typos are corrected here. There are also font and other typographical differences that mean the page numbers do not match between the versions.  \nContents  \nContents page ii  \nPart I Bandits, Probability and Concentration 7  \n1 Introduction 8  \n1.1 The Language of Bandits 10  \n1.2 Applications 13  \n1.3 Notes 16  \n1.4 Bibliographic Remarks 16  \n2 Foundations of Probability () 18  \n2.1 Probability Spaces and Random Elements 18  \n2.2 σ-Algebras and Knowledge 26  \n2.3 Conditional Probabilities 28  \n2.4 Independence 29  \n2.5 Integration and Expectation 30  \n2.6 Conditional Expectation 33  \n2.7 Notes 37  \n2.8 Bibliographic Remarks 42  \n2.9 Exercises 42  \n3 Stochastic Processes and Markov Chains () 46  \n3.1 Stochastic Processes 47  \n3.2 Markov Chains 48  \n3.3 Martingales and Stopping Times 49  \n3.4 Notes 52  \n3.5 Bibliographic Remarks 53  \n3.6 Exercises 54  \n4 Stochastic Bandits 56  \n4.1 Core Assumptions 56  \n4.2 The Learning Objective 57  \n4.3 Knowledge and Environment Classes 57  \n4.4 The Regret 60  \n4.5 Decomposing the Regret 62  \n4.6 The Canonical Bandit Model () 63  \n4.7 The Canonical Bandit Model for Uncountable Action Sets () 66  \n4.8 Notes 66  \n4.9 Bibliographical Remarks 68  \n4.10 Exercises 69  \n5 Concentration of Measure 74  \n5.1 Tail Probabilities 74  \n5.2 The Inequalities of Markov and Chebyshev 75  \n5.3 The Cram´er-Chernoff Method and Subgaussian Random Variables 77  \n5.4 Notes 79  \n5.5 Bibliographical Remarks 81  \n5.6 Exercises 81  \nPart II Stochastic Bandits with Finitely Many Arms 89  \n6 The Explore-Then-Commit Algorithm 91  \n6.1 Algorithm and Regret Analysis 91  \n6.2 Notes 95  \n6.3 Bibliographical Remarks 95  \n6.4 Exercises 96  \n7 The Upper Confidence Bound Algorithm 102  \n7.1 The Optimism Principle 102  \n7.2 Notes 110  \n7.3 Bibliographical Remarks 111  \n7.4 Exercises 111  \n8 The Upper Confidence Bound Algorithm: Asymptotic Optimality 117  \n8.1 Asymptotically Optimal UCB 117  \n8.2 Notes 120  \n8.3 Bibliographic Remarks 120  \n8.4 Exercises 121  \n9 The Upper Confidence Bound Algorithm: Minimax Optimality () 123  \n9.1 The MOSS Algorithm 123  \n9.2 Two Problems 127  \n9.3 Notes 128  \n9.4 Bibliographic Remarks 129  \n9.5 Exercises 129  \n10 The Upper Confidence Bound Algorithm: Bernoulli Noise () 133  \n10.1 Concentration for Sums of Bernoulli Random Variables 133  \n10.2 The KL-UCB Algorithm 137  \n10.3 Notes 140  \n10.4 Bibliographic Remarks 141  \n10.5 Exercises 141  \nPart III Adversarial Bandits with Finitely Many Arms 144  \n11 The Exp3 Algorithm 148  \n11.1 Adversarial Bandit Environments 148  \n11.2 Importance-Weighted Estimators 150  \n11.3 The Exp3 Algorithm 152  \n11.4 Regret Analysis 153  \n11.5 Notes 157  \n11.6 Bibliographic Remarks 160  \n11.7 Exercises 160  \n12 The Exp3-IX Algorithm 165  \n12.1 The Exp3-IX Algorithm 165  \n12.2 Regret Analysis 167  \n12.3 Notes 171  \n12.4 Bibliographic Remarks 172  \n12.5 Exercises 172  \nPart IV Lower Bounds for Bandits with Finitely Many Arms 177  \n13 Lower Bounds: Basic Ideas 180  \n13.1 Main Ideas Underlying Minimax Lower Bounds 181  \n13.2 Notes 183  \n13.3 Bibliographic Remarks 184  \n13.4 Exercises 184  \n14 Foundations of Information Theory () 186  \n14.1 Entropy and Optimal Coding 186  \n14.2 Relative Entropy 188  \n14.3 Notes 191  \n14.4 Bibliographic Remarks 194  \n14.5 Exercises 194  \n15 Minimax Lower Bounds 198  \n15.1 Relative Entropy Between Bandits 198  \n15.2 Minimax Lower Bounds 199  \n15.3 Notes 201  \n15.4 Bibliographic Remarks 203  \n15.5 Exercises 203  \n16 Instance-Dependent Lower Bounds 206  \n16.1 Asymptotic Bounds 207  \n16.2 Finite-Time Bounds 209  \n16.3 Notes 210  \n16.4 Bibliographic Remarks 211  \n16.5 Exercises 211  \n17 High-Probability Lower Bounds 215  \n17.1 Stochastic Bandits 216  \n17.2 Adversarial Bandits 218  \n17.3 Notes 220  \n17.4 Bibliographic Remarks 220  \n17.5 Exercises 221  \nPart V Contex","cbCaitbZDkDOxGVq","https://ap.wps.com/l/cbCaitbZDkDOxGVq","pdf",5400750,597,"English","# Part I Bandits, Probability and Concentration\n## 1 Introduction\n## 2 Foundations of Probability\n## 3 Stochastic Processes and Markov Chains\n## 4 Stochastic Bandits\n## 5 Concentration of Measure\n# Part II Stochastic Bandits with Finitely Many Arms\n## 6 The Explore-Then-Commit Algorithm\n## 7 The Upper Confidence Bound Algorithm\n## 8 The Upper Confidence Bound Algorithm: Asymptotic Optimality\n## 9 The Upper Confidence Bound Algorithm: Minimax Optimality\n## 10 The Upper Confidence Bound Algorithm: Bernoulli Noise\n# Part III Adversarial Bandits with Finitely Many Arms\n## 11 The Exp3 Algorithm\n## 12 The Exp3-IX Algorithm\n# Part IV Lower Bounds for Bandits with Finitely Many Arms\n## 13 Lower Bounds: Basic Ideas\n## 14 Foundations of Information Theory\n## 15 Minimax Lower Bounds\n## 16 Instance-Dependent Lower Bounds\n## 17 High-Probability Lower Bounds\n# Part V Contextual and Linear Bandits\n## 18 Contextual Bandits\n## 19 Stochastic Linear Bandits\n## 20 Confidence Bounds for Least Squares Estimators\n## 21 Optimal Design for Least Squares Estimators\n## 22 Stochastic Linear Bandits with Finitely Many Arms\n## 23 Stochastic Linear Bandits with Sparsity\n## 24 Minimax Lower Bounds for Stochastic Linear Bandits\n## 25 Asymptotic Lower Bounds for Stochastic Linear Bandits\n# Part VI Adversarial Linear Bandits\n## 26 Foundations of Convex Analysis","[{\"question\":\"What core concepts does the book cover for bandit problems?\",\"answer\":\"The book builds on probability spaces, conditional probability, independence, expectation, stochastic processes, Markov chains, martingales, stopping times, and concentration of measure. These tools support regret analysis across multiple bandit settings.\"},{\"question\":\"How does the book treat stochastic bandits with finitely many arms?\",\"answer\":\"It analyzes algorithms such as Explore-Then-Commit and Upper Confidence Bound (UCB) variants, including asymptotic and minimax optimality perspectives and specialized analyses like Bernoulli noise. It also decomposes regret to support the theoretical results.\"},{\"question\":\"How are adversarial bandits and lower bounds handled?\",\"answer\":\"Adversarial bandits are addressed with algorithms like Exp3 and Exp3-IX under adversarial bandit environments and importance-weighted estimators. Lower bounds are derived using information-theoretic foundations such as entropy and relative entropy, then extended to minimax, instance-dependent, and high-probability forms.\"}]","Bandit Algorithms | PDF",1504]