[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-128859-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-128859-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","block-coordinate-frank-wolfe-optimization-for-structural-svms","Block-Coordinate Frank-Wolfe Optimization for Structural SVMs","","A randomized block-coordinate variant of the classic Frank-Wolfe algorithm is developed for convex optimization with block-separable constraints. Although each iteration is cheaper, the method attains a convergence rate in duality gap comparable to full Frank-Wolfe. Applied to the dual structural SVM objective, it yields an online algorithm with iteration complexity similar to primal stochastic subgradient methods. Unlike stochastic subgradient training, it enables closed-form optimal step-size selection and provides a computable duality-gap stopping guarantee. Experiments show superior performance versus competing structural SVM solvers.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/block-coordinate-frank-wolfe-optimization-for-structural-svms/128859/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/block-coordinate-frank-wolfe-optimization-for-structural-svms/128859.png","ImageObject",300,407,{"name":42,"@type":43},"Noah","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-09-19","2026-08-06",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What problem does the randomized block-coordinate Frank-Wolfe method target?","Question",{"text":63,"@type":64},"It targets convex optimization problems with block-separable constraints, using a randomized block-coordinate variant to reduce iteration cost.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does the method compare with full Frank-Wolfe in convergence?",{"text":68,"@type":64},"It achieves a similar convergence rate in duality gap to the full Frank-Wolfe algorithm despite using lower-cost iterations.",{"name":70,"@type":61,"acceptedAnswer":71},"What advantages does this approach provide for training dual structural SVMs?",{"text":72,"@type":64},"It produces an online algorithm with low iteration complexity like primal stochastic subgradient methods, while offering closed-form optimal step-size and a computable duality gap guarantee for stopping.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},128859,1786003990,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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Normale Sup􀀓erieure, Paris, France  \nMartin Jaggi􀀃 CMAP, cole Polytechnique, Palaiseau, France  \n􀀓  \nMark Schmidt INRIA-SIERRA project-team, Ecole Normale Sup􀀓erieure, Paris, France  \nPatrick Pletscher Machine Learning Laboratory, ETH Zurich, Switzerland  \n􀀃 Both authors contributed equally.  \nAbstract  \nWe propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full FrankWolfe algorithm. We also show that, when applied to the dual structural support vector machine (SVM) objective, this yields an online algorithm that has the same low iteration complexity as primal stochastic subgradient methods. However, unlike stochastic subgradient methods, the block-coordinate FrankWolfe algorithm allows us to compute the optimal step-size and yields a computable duality gap guarantee. Our experiments indicate that this simple algorithm outperforms competing structural SVM solvers.  \n1. Introduction  \nBinary SVMs are amongst the most popular classi􀀌cation methods, and this has motivated substantial interest in optimization solvers that are tailored to their speci􀀌c problem structure. However, despite their wider applicability, there has been much less work on solving the optimization problem associated with structural SVMs, which are the generalization of SVMs to structured outputs like graphs and other combinatorial objects (Taskar et al. , 2003; Tsochantaridis et al. , 2005) . This seems to be due to the di􀀎culty of dealing with the exponential number of constraints in the primal problem, or the exponential number of variables in~ the dual problem. Indeed, because they achieve an O(1=\") convergence rate while only requiring a single  \nProceedings of the 30 th International Conference on Machine Learning, Atlanta, Georgia, USA, 2013 . JMLR: W&CP volume 28 . Copyright 2013 by the author(s) .  \ncall to the so-called maximization oracle on each iteration, basic stochastic subgradient methods are still widely used for training structural SVMs (Ratli􀀋 et al. , 2007; Shalev-Shwartz et al. , 2010a) . However, these methods are often frustrating to use for practitioners, because their performance is very sensitive to the sequence of step sizes, and because it is di􀀎cult to decide when to terminate the iterations.  \nTo solve the dual structural SVM problem, in this paper we consider the Frank-Wolfe (1956) algorithm, which has seen a recent surge of interest in machine learning and signal processing (Mangasarian, 1995; Clarkson, 2010; Jaggi, 2011; 2013; Bach et al. , 2012), including in the context of binary SVMs (G􀁿artner & Jaggi, 2009; Ouyang & Gray, 2010) . A key advantage of this algorithm is that the iterates are sparse, and we show that this allows us to e􀀎ciently apply it to the dual structural SVM objective even though there are an exponential number of variables. A second key advantage of this algorithm is that the iterations only require optimizing linear functions over the constrained domain, and we show that this is equivalent to the maximization oracle used by subgradient and cutting-plane methods (Joachims et al. , 2009; Teo et al. , 2010) . Thus, the Frank-Wolfe algorithm has the same wide applicability as subgradient methods, and can be applied to problems such as low-treewidth graphical models (Taskar et al. , 2003), graph matchings (Caetano et al. , 2009), and associative Markov networks (Taskar, 2004) . In contrast, other approaches must use more expensive (and potentially intractable) oracles such as computing marginalsover labels (Collins et al. , 2008; Zhang et al. , 2011) or doing a Bregman projection onto the space of structures (Taskar et al. , 2006) . Interestingly, for structural SVMs we also show that existing batch","cbCaifMbUR8JYq2o","https://ap.wps.com/l/cbCaifMbUR8JYq2o","pdf",1940268,31,"English","# Introduction\n## Structural Support Vector Machines\n## Block-Coordinate Frank-Wolfe Algorithm\n## Online Dual Structural SVM Training\n## Experimental Results","[{\"question\":\"What problem does the randomized block-coordinate Frank-Wolfe method target?\",\"answer\":\"It targets convex optimization problems with block-separable constraints, using a randomized block-coordinate variant to reduce iteration cost.\"},{\"question\":\"How does the method compare with full Frank-Wolfe in convergence?\",\"answer\":\"It achieves a similar convergence rate in duality gap to the full Frank-Wolfe algorithm despite using lower-cost iterations.\"},{\"question\":\"What advantages does this approach provide for training dual structural SVMs?\",\"answer\":\"It produces an online algorithm with low iteration complexity like primal stochastic subgradient methods, while offering closed-form optimal step-size and a computable duality gap guarantee for stopping.\"}]","Block-Coordinate Frank-Wolfe Optimization for Structural SVMs | PDF",78]