[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82940-en":3,"doc-seo-82940-105":29,"detail-sidebar-cat-0-en-105":82},{"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":13,"seo_description":14,"update_tm":27,"read_time":28},82940,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Graph Sparse Sampling Breaking the Curse of the Horizon in Continuous MDP Planning","Planning under uncertainty in continuous domains is central to autonomous systems but can be computationally prohibitive. Tree-based methods like Monte Carlo Tree Search often require sampling budgets that scale exponentially with lookahead depth due to their branching structure, especially with infinite branching in continuous state or action spaces. Graph Sparse Sampling (GSS) is an online planning algorithm that shares sampled futures across many candidate decisions, forming a graph without branching to enable GPU-friendly batching and heuristic-focused computation. Finite-sample, polynomial-in-horizon guarantees are proven under overlap and coverage conditions, including full-rank or low-rank simulators and discrete or sampled continuous actions.","arXiv :2607 .05359v 1 [ cs .AI] 6 Jul 2026  \nGraph Sparse Sampling: Breaking the Curse of the Horizon in Continuous MDP Planning  \nIdan Lev-Yehudi 1 Vadim Indelman2 ,3  \n1Technion Autonomous Systems Program (TASP), Technion – Israel Institute of Technology  \n2 Stephen B. Klein Faculty of Aerospace Engineering, Technion – Israel Institute of Technology  \n3Faculty of Data and Decision Sciences, Technion – Israel Institute of Technology  \n[idanlev@campus.technion.ac.il](idanlev@campus.technion.ac.il) , [vadim.indelman@technion.ac.il](vadim.indelman@technion.ac.il)  \nAbstract  \nPlanning under uncertainty in continuous domains is essential for autonomous systems, yet computationally demanding. Tree-based search methods such as Monte Carlo Tree Search (MCTS) remain popular, but their branching structure can require sampling budgets that grow exponentially with lookahead depth in the worst case. From a tree perspective, continuous state or action spaces become especially challenging, since the planner must decide where to search in an infinite branching hierarchy. We propose Graph Sparse Sampling (GSS), an online planning algorithm that shares sampled futures across many candidate decisions, rather than sampling separate successors for each candidate action. This branch-free graph exposes large GPU-friendly batches, while using heuristics to focus computation.  \nWe prove finite-sample performance guarantees for GSS covering full-rank or low-rank generative simulators via smoothed backups, and discrete or sampled continuous action spaces. Under suitable overlap, regularity, and action-coverage conditions, these bounds have polynomial dependence on the planning horizon, formalizing when shared futures can avoid the exponential horizon dependence of tree-shaped sparse sampling. We demonstrate continuous-control simulations where GSS substantially outperforms tree-based planners on long horizons or achieves near-optimal performance, supporting no-branching graph planning as a complementary design principle for online control.  \n1 Introduction  \nPlanning under uncertainty is a fundamental problem in artificial intelligence, and continuous Markov Decision Processes (MDPs) model many physical systems. For discrete MDPs, exact policy computation is computationally constrained: finite-horizon, discounted, and average-cost variants are polynomial-time solvable but P-complete [Papadimitriou and Tsitsiklis, 1987] . Continuous MDPs add a difficulty, since neither the state space nor the action space can be enumerated directly. Sparse Sampling [Kearns et al., 2002] addresses large state spaces by using only a generative model to sample a sparse set of successor states at each state-action pair, yielding online planning bounds independent of the state dimension. However, these are exponential in the effective planning horizon, and worst-case tight when only a black-box simulator is available [Kearns et al., 2002] .  \nMost practical continuous MDP planners build a search tree, and adapt how the tree is widened or how actions are selected. Double Progressive Widening (DPW) [Couëtoux et al., 2011] limits the number of state and action children in continuous Monte Carlo Tree Search; KR-UCT [Yee et al., 2016] shares value estimates between nearby continuous actions; Voronoi Optimistic Optimization (VOO) and VOOT [Kim et al., 2020] use Voronoi-based black-box optimization inside tree search; and VG-UCT [Lee et al., 2020] refines sampled actions using value gradients. Other non-tree approaches include Model Predictive Path Integral control (MPPI) [Williams et al., 2017], which optimizes  \nPreprint.  \nsampled open-loop trajectories with importance-weighted path costs, and stochastic mesh method (SMM) [Broadie et al., 2004] and weighted stochastic mesh (WSM) [Belomestny et al., 2020, 2025], which reuse sampled states in problems such as high-dimensional option pricing and general Markov decision processes. These methods provide important ways to cope with c","cbCaibWIZaeC8qI8","https://ap.wps.com/l/cbCaibWIZaeC8qI8","pdf",1109158,1,23,"English","en",105,"# Introduction\n## Main Contributions\n# Algorithm: Graph Sparse Sampling\n## Theoretical Guarantees\n## Empirical Evaluation","[{\"question\":\"What theoretical results are provided for GSS?\",\"answer\":\"GSS comes with finite-sample, high-probability performance guarantees for action-value estimates, with polynomial dependence on the planning horizon under overlap, backup-stability, and action-coverage conditions, with extensions to continuous actions and low-rank generative simulators.\"}]",1784184171,58,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":77,"head_meta":79,"extra_data":81,"updated_unix":27},"graph-sparse-sampling-breaking-the-curse-of-the-horizon-in-continuous-mdp-planning","",{"@graph":35,"@context":76},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/graph-sparse-sampling-breaking-the-curse-of-the-horizon-in-continuous-mdp-planning/82940/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70],{"name":71,"@type":72,"acceptedAnswer":73},"What theoretical results are provided for GSS?","Question",{"text":74,"@type":75},"GSS comes with finite-sample, high-probability performance guarantees for action-value estimates, with polynomial dependence on the planning horizon under overlap, backup-stability, and action-coverage conditions, with extensions to continuous actions and low-rank generative simulators.","Answer","https://schema.org",{"og:url":51,"og:type":78,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":80,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":83},[84,88,92,96,101,106,111,114,119,122,126],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":45,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":45,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":112,"slug":113},30,"research-report",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":45,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":97,"slug":129},19,"General","general"]