[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657526-105":59,"doc-detail-657526-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","spudd-stochastic-planning-using-decision-diagrams","SPUDD - Stochastic Planning using Decision Diagrams","","Recently, structured methods have been developed to solve factored Markov decision processes with large state spaces without enumerating every state. SPUDD introduces a value iteration algorithm that represents value functions and policies using algebraic decision diagrams (ADDs), given an ADD representation of the MDP. Dynamic programming is carried out through ADD manipulation, achieving exact solutions on very large problems and demonstrating major reductions versus tree-based representations.",{"@graph":69,"@context":122},[70,84,105],{"@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/spudd-stochastic-planning-using-decision-diagrams/657526/",{"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/spudd-stochastic-planning-using-decision-diagrams/657526.png","ImageObject",300,407,{"name":92,"@type":93},"Alex Sinclair","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does SPUDD address?","Question",{"text":112,"@type":113},"SPUDD targets solving factored MDPs with large state spaces, where classical dynamic programming is hindered by the need for complete state enumeration.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does SPUDD represent value functions and policies?",{"text":117,"@type":113},"It represents value functions and policies using algebraic decision diagrams (ADDs) rather than tabular forms.",{"name":119,"@type":110,"acceptedAnswer":120},"How is dynamic programming performed in SPUDD?",{"text":121,"@type":113},"Dynamic programming is implemented via ADD manipulation, enabling compact computation and reduced work compared with tree-structured representations.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657526,1792981965,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","SPUDD: Stochastic Planning using Decision Diagrams  \nJesse Hoey Robert St-Aubin Alan Hu Craig Boutilier  \nDepartment of Computer Science University of British Columbia Vancouver, BC, V6T 1Z4, CANADA fjhoey,staubin,ajh,[cebly](ceblyg@cs.ubc.ca)[g](ceblyg@cs.ubc.ca)[@cs.ubc.ca](ceblyg@cs.ubc.ca)  \nAbstract  \nRecently, structured methods for solving factored Markov decisions processes (MDPs) with large state spaces have been proposed recently to allow dynamic programming to be applied without the need for complete state enumeration. We propose and examine a new value iteration algorithm for MDPs that uses algebraic decision diagrams (ADDs) to represent value functions and policies, assuming an ADD input representation of the MDP. Dynamic programming is implemented via ADD manipulation. We demonstrate our method on a class of large MDPs (up to 63 million states) and show that significant gains can be had when compared to tree-structured representations (with up to a thirty-fold reduction in the number of nodes required to represent optimal value functions) .  \n1 Introduction  \nMarkov decision processes (MDPs) have become the semantic model of choice for decision theoretic planning (DTP) in the AI planning community. While classical computational methods for solving MDPs, such as value iteration and policy iteration [19], are often effective for small problems, typical AI planning problems fall prey to Bellman’s curse of dimensionality: the size of the state space grows exponentially with the number of domain features. Thus, classical dynamic programming, which requires explicit enumeration of the state space, is typically infeasible for feature-based planning problems.  \nConsiderable effort has been devoted to developing representational and computational methods for MDPs that obviate the need to enumerate the state space [5] . Aggregation methods do this by aggregating a set of states and treating the states within any aggregate state as if they were identical [3] . Within AI, abstraction techniques have been widely studied as a form of aggregation, where states are (implicitly) grouped by ignoring certain problem variables [14, 7, 12] . These methods automatically generate abstract MDPs by exploiting structured representations, such as probabilistic STRIPS rules [16] or dynamic Bayesian network (DBN) representations of actions [13, 7] .  \nIn this paper, we describe a dynamic abstraction method for solving MDPs using algebraic decision diagrams (ADDs)  \n[1] to represent value functions and policies. ADDs are generalizations of ordered binary decision diagrams (BDDs) [10] that allow non-boolean labels at terminal nodes. This representational technique allows one to describe a value function (or policy) as a function of the variables describing the domain rather than in the classical “tabular” way. The decision graph used to represent this function is often extremely compact, implicitly grouping together states that agree on value at different points in the dynamic programming computation. As such, the number of expected value computations and maximizations required by dynamic programming are greatly reduced. The algorithm described here derives from the structured policy iteration (SPI) algorithm of [7, 6, 4], where decision trees are used to represent value functions and policies. Given a DBN action representation (with decision trees used to represent conditional probability tables) anda decision tree representation of the reward function, SPI constructs value functions that preserve much ofthe DBN structure. Unfortunately, decision trees cannot compactly represent certain types of value functions, especially those that involve disjunctive value assessments. For instance, if the proposition a_b_c describes a group of states that have a specific value, a decision tree must duplicate that value three times (and in SPI the value is computed three times) . Furthermore, if the proposition describes not a single value, but rather identi","cbCaiirDk1ayEDEj","https://ap.wps.com/l/cbCaiirDk1ayEDEj","pdf",187207,"English","# Introduction\n## Markov Decision Processes\n# SPUDD and Algebraic Decision Diagrams\n## ADD Representation and Value Iteration\n## Empirical Results\n# Conclusion","[{\"question\":\"What problem does SPUDD address?\",\"answer\":\"SPUDD targets solving factored MDPs with large state spaces, where classical dynamic programming is hindered by the need for complete state enumeration.\"},{\"question\":\"How does SPUDD represent value functions and policies?\",\"answer\":\"It represents value functions and policies using algebraic decision diagrams (ADDs) rather than tabular forms.\"},{\"question\":\"How is dynamic programming performed in SPUDD?\",\"answer\":\"Dynamic programming is implemented via ADD manipulation, enabling compact computation and reduced work compared with tree-structured representations.\"}]","SPUDD - Stochastic Planning using Decision Diagrams | PDF",25]