[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124561-en":3,"doc-seo-124561-105":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},124561,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Online Learning of Network Bottlenecks via Minimax Paths","This paper studies bottleneck identification in networks by extracting minimax paths. Real-world networks often have stochastic edge weights with limited prior knowledge, so the task is formulated as a combinatorial semi-bandit problem. A combinatorial Thompson Sampling method is introduced and an upper bound on Bayesian regret is proved. To address computational intractability, an alternative approximation formulation is proposed and analyzed. Experiments on directed and undirected real-world networks evaluate Thompson Sampling using the approximate setup.","Online Learning of Network Bottlenecks via Minimax Paths  \nNiklas A˚ kerblom, 1, 2,* Fazeleh Sadat Hoseini, 1,* Morteza Haghir Chehreghani 1  \n1 Chalmers University of Technology  \n2 Volvo Car Corporation  \n[niklas.akerblom@chalmers.se](niklas.akerblom@chalmers.se), [fazeleh@chalmers.se](fazeleh@chalmers.se), [morteza.chehreghani@chalmers.se](morteza.chehreghani@chalmers.se)  \narXiv :2 109 .08467v2 [ cs .LG] 16 Nov 2021  \nAbstract  \nIn this paper, we study bottleneck identification in networks via extracting minimax paths. Many real-world networks have stochastic weights for which full knowledge is not available in advance. Therefore, we model this task as a combinatorial semi-bandit problem to which we apply a combinatorial version of Thompson Sampling and establish an upper bound on the corresponding Bayesian regret. Due to the computational intractability of the problem, we then devise an alternative problem formulation which approximates the original objective. Finally, we experimentally evaluate the performance of Thompson Sampling with the approximate formulation on real-world directed and undirected networks.  \n1 Introduction  \nBottleneck identification constitutes an important task in network analysis, with applications including transportation planning and management (Berman and Handler 1987), routing in computer networks (Shacham 1992) and various bicriterion path problems (Hansen 1980) . The path-specific bottleneck, on a path between a source and a target node in a network, is defined as the edge with a maximal cost or weight according to some criterion such as transfer time, load, commute time, distance, etc. The goal of bottleneck identification and avoidance is then to find a path whose bottleneck is minimal. Thus, one may model bottleneck identification as the problem of computing the minimax edge over the given network/graph, to obtain an edge with a minimal largest gap between the source and target nodes. Equivalently, it can be formulated as a widest path problem or maximum capacity path problem (Pollack 1960) where the edge weights have been negated.  \nThe aforementioned formulations assume that the network or the graph is fully specified, i.e., that all the edge weights are fully known. However, in practice, the edge weights might not be known in advance or they might include some inherent uncertainty. In this paper, we tackle such situations by developing an online learning framework to learn the edge weight distributions of the underlying network, while solving the bottleneck identification problem for different problem instances. For this purpose, we view this as a multi-armed bandit (MAB) problem and focus on  \n*These authors contributed equally.  \nThompson Sampling (TS) (Thompson 1933), a method that suits probabilistic online learning well.  \nThompson Sampling is an early Bayesian method for addressing the trade-off between exploration and exploitation in sequential decision making problems. It has only recently been thoroughly evaluated through experimental studies (Chapelle and Li 2011; Graepel et al. 2010) and theoretical analyses (Kaufmann, Korda, and Munos 2012; Agrawal and Goyal 2012; Russo and Van Roy 2014), where it has been shown to be asymptotically optimal in the sense that it matches well-known lower bounds of these types of problems (Lai and Robbins 1985) .  \nAmong many other problem settings, Thompson Sampling has been adapted to online versions of combinatorial optimization problems with retained theoretical guarantees (Wang and Chen 2018), where one application is to find shortest paths in graphs (Liu and Zhao 2012; Gai, Krishnamachari, and Jain 2012; Zou, Proutiere, and Johansson 2014; A˚ kerblom, Chen, and Chehreghani 2020) .  \nAnother commonly used method for these problems is Upper Confidence Bound (UCB) (Auer 2002), which utilizes optimism to balance exploration and exploitation. UCB has been adapted to combinatorial settings (Chen, Wang, and Yuan 2013), and also exists in Bayesian variants","cbCaiqqW78DHym29","https://ap.wps.com/l/cbCaiqqW78DHym29","pdf",2253185,1,16,"English","en",105,"# Introduction\n## Bottleneck identification and minimax path formulations\n## Online learning under uncertain edge weights\n## Thompson Sampling and related methods\n# Bottleneck Identification Model\n## Bottleneck identification on a fixed network\n## Probabilistic modeling for stochastic and uncertain cases","[{\"question\":\"How is the bottleneck identification problem defined for a network path?\",\"answer\":\"The bottleneck on a path is the edge with the maximal cost/weight under a chosen criterion, and the objective is to find a path whose bottleneck is minimal.\"},{\"question\":\"Why is online learning needed in this setting?\",\"answer\":\"In practice, edge weights may be unknown in advance or include uncertainty, so the framework learns edge weight distributions while solving bottleneck identification for different instances.\"},{\"question\":\"What method does the paper use to balance exploration and exploitation?\",\"answer\":\"The paper applies a combinatorial variant of Thompson Sampling to the stochastic combinatorial semi-bandit formulation and provides an upper bound on Bayesian regret.\"}]","Online Learning of Network Bottlenecks via Minimax Paths | 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is the bottleneck identification problem defined for a network path?","Question",{"text":75,"@type":76},"The bottleneck on a path is the edge with the maximal cost/weight under a chosen criterion, and the objective is to find a path whose bottleneck is minimal.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is online learning needed in this setting?",{"text":80,"@type":76},"In practice, edge weights may be unknown in advance or include uncertainty, so the framework learns edge weight distributions while solving bottleneck identification for different instances.",{"name":82,"@type":73,"acceptedAnswer":83},"What method does the paper use to balance exploration and exploitation?",{"text":84,"@type":76},"The paper applies a combinatorial variant of Thompson Sampling to the stochastic combinatorial semi-bandit formulation and provides an upper bound on Bayesian 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