Relevant bibliographies by topics / Frank-Wolfe Method

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Frank-Wolfe Method'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Frank-Wolfe Method"

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Zahavy, Tom, Alon Cohen, Haim Kaplan, and Yishay Mansour. "Apprenticeship Learning via Frank-Wolfe." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6720–28. http://dx.doi.org/10.1609/aaai.v34i04.6150.

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We consider the applications of the Frank-Wolfe (FW) algorithm for Apprenticeship Learning (AL). In this setting, we are given a Markov Decision Process (MDP) without an explicit reward function. Instead, we observe an expert that acts according to some policy, and the goal is to find a policy whose feature expectations are closest to those of the expert policy. We formulate this problem as finding the projection of the feature expectations of the expert on the feature expectations polytope – the convex hull of the feature expectations of all the deterministic policies in the MDP. We show that this formulation is equivalent to the AL objective and that solving this problem using the FW algorithm is equivalent well-known Projection method of Abbeel and Ng (2004). This insight allows us to analyze AL with tools from convex optimization literature and derive tighter convergence bounds on AL. Specifically, we show that a variation of the FW method that is based on taking “away steps” achieves a linear rate of convergence when applied to AL and that a stochastic version of the FW algorithm can be used to avoid precise estimation of feature expectations. We also experimentally show that this version outperforms the FW baseline. To the best of our knowledge, this is the first work that shows linear convergence rates for AL.
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Freund, Robert M., and Paul Grigas. "New analysis and results for the Frank–Wolfe method." Mathematical Programming 155, no. 1-2 (November 28, 2014): 199–230. http://dx.doi.org/10.1007/s10107-014-0841-6.

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FRANDI, EMANUELE, RICARDO ÑANCULEF, MARIA GRAZIA GASPARO, STEFANO LODI, and CLAUDIO SARTORI. "TRAINING SUPPORT VECTOR MACHINES USING FRANK–WOLFE OPTIMIZATION METHODS." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 03 (May 2013): 1360003. http://dx.doi.org/10.1142/s0218001413600033.

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Training a support vector machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be directly applied in these cases, mainly due to memory restrictions. By adopting a slightly different objective function and under mild conditions on the kernel used within the model, efficient algorithms to train SVMs have been devised under the name of core vector machines (CVMs). This framework exploits the equivalence of the resulting learning problem with the task of building a minimal enclosing ball (MEB) problem in a feature space, where data is implicitly embedded by a kernel function. In this paper, we improve on the CVM approach by proposing two novel methods to build SVMs based on the Frank–Wolfe algorithm, recently revisited as a fast method to approximate the solution of a MEB problem. In contrast to CVMs, our algorithms do not require to compute the solutions of a sequence of increasingly complex QPs and are defined by using only analytic optimization steps. Experiments on a large collection of datasets show that our methods scale better than CVMs in most cases, sometimes at the price of a slightly lower accuracy. As CVMs, the proposed methods can be easily extended to machine learning problems other than binary classification. However, effective classifiers are also obtained using kernels which do not satisfy the condition required by CVMs, and thus our methods can be used for a wider set of problems.
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Migdalas, Athanasios. "A regularization of the Frank—Wolfe method and unification of certain nonlinear programming methods." Mathematical Programming 65, no. 1-3 (February 1994): 331–45. http://dx.doi.org/10.1007/bf01581701.

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Kherad, Mahdi, Hamed Vahdat-Nejad, and Morteza Araghi. "Trasfugen: Traffic assignment of urban network by an approximation fuzzy genetic algorithm." International Journal of Modeling, Simulation, and Scientific Computing 09, no. 04 (August 2018): 1850034. http://dx.doi.org/10.1142/s1793962318500344.

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This paper proposes the Trasfugen method for traffic assignment aimed at solving the user equilibrium problem. To this end, the method makes use of a genetic algorithm. A fuzzy system is proposed for controlling the mutation and crossover rates of the genetic algorithm, and the corrective strategy is exploited for handling the equilibrium problem constraints. In the model, an approximation algorithm is proposed for obtaining the paths between the origin–destination pairs in the demand matrix. Unlike the traditional deterministic algorithm that has exponential time complexity, this approximation algorithm has polynomial time complexity and is executed much faster. Afterward, the Trasfugen method is applied to the urban network of Tehran metropolitan and the efficiency is investigated. Upon comparing the results obtained from the proposed model with those obtained from the conventional traffic assignment method, namely, the Frank–Wolfe method; it is shown that the proposed algorithm, while acting worse during the initial iterations, achieves better results in the subsequent iterations. Moreover, it prevents the occurrence of local optimal points as well as early/premature convergence, thus producing better results than the Frank–Wolfe algorithm.
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Chryssoverghi, I., A. Bacopoulos, B. Kokkinis, and J. Coletsos. "Mixed Frank–Wolfe Penalty Method with Applications to Nonconvex Optimal Control Problems." Journal of Optimization Theory and Applications 94, no. 2 (August 1997): 311–34. http://dx.doi.org/10.1023/a:1022631611812.

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Xu, Jianhua, and Quan Ma. "Multi-label regularized quadratic programming feature selection algorithm with Frank–Wolfe method." Expert Systems with Applications 95 (April 2018): 14–31. http://dx.doi.org/10.1016/j.eswa.2017.11.018.

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Tatineni, Maya, Henrik Edwards, and David Boyce. "Comparison of Disaggregate Simplicial Decomposition and Frank-Wolfe Algorithms for User-Optimal Route Choice." Transportation Research Record: Journal of the Transportation Research Board 1617, no. 1 (January 1998): 157–62. http://dx.doi.org/10.3141/1617-22.

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The disaggregate simplicial decomposition (DSD) method has been posed as a better alternative to existing algorithms for solving the deterministic user-optimal route choice model. The application of the DSD algorithm is compared and evaluated with the commonly used Frank-Wolfe (FW) algorithm on a large network in the Chicago area. The results indicate that the DSD algorithm performs much better than the FW with respect to reaching the optimality conditions specified by the model.
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Nakamura, Kengo, Shinsaku Sakaue, and Norihito Yasuda. "Practical Frank–Wolfe Method with Decision Diagrams for Computing Wardrop Equilibrium of Combinatorial Congestion Games." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 02 (April 3, 2020): 2200–2209. http://dx.doi.org/10.1609/aaai.v34i02.5596.

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Computation of equilibria for congestion games has been an important research subject. In many realistic scenarios, each strategy of congestion games is given by a combination of elements that satisfies certain constraints; such games are called combinatorial congestion games. For example, given a road network with some toll roads, each strategy of routing games is a path (a combination of edges) whose total toll satisfies a certain budget constraint. Generally, given a ground set of n elements, the set of all such strategies, called the strategy set, can be large exponentially in n, and it often has complicated structures; these issues make equilibrium computation very hard. In this paper, we propose a practical algorithm for such hard equilibrium computation problems. We use data structures, called zero-suppressed binary decision diagrams (ZDDs), to compactly represent strategy sets, and we develop a Frank–Wolfe-style iterative equilibrium computation algorithm whose per-iteration complexity is linear in the size of the ZDD representation. We prove that an ϵ-approximate Wardrop equilibrium can be computed in O(poly(n)/ϵ) iterations, and we improve the result to O(poly(n) log ϵ−1) for some special cases. Experiments confirm the practical utility of our method.
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Kubentayeva, Meruza, and Alexander Gasnikov. "Finding Equilibria in the Traffic Assignment Problem with Primal-Dual Gradient Methods for Stable Dynamics Model and Beckmann Model." Mathematics 9, no. 11 (May 27, 2021): 1217. http://dx.doi.org/10.3390/math9111217.

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In this paper, we consider the application of several gradient methods to the traffic assignment problem: we search equilibria in the stable dynamics model (Nesterov and De Palma, 2003) and the Beckmann model. Unlike the celebrated Frank–Wolfe algorithm widely used for the Beckmann model, these gradients methods solve the dual problem and then reconstruct a solution to the primal one. We deal with the universal gradient method, the universal method of similar triangles, and the method of weighted dual averages and estimate their complexity for the problem. Due to the primal-dual nature of these methods, we use a duality gap in a stopping criterion. In particular, we present a novel way to reconstruct admissible flows in the stable dynamics model, which provides us with a computable duality gap.
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Dissertations / Theses on the topic "Frank-Wolfe Method"

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Högdahl, Johan. "Conditional steepest descent directions over Cartesian product sets : With application to the Frank-Wolfe method." Thesis, Linköpings universitet, Optimeringslära, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-123730.

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We derive a technique for scaling the search directions of feasible direction methods when applied to optimization problems over Cartesian product sets. It is proved that when the scaling is included in a convergent feasible direction method, also the new method will be convergent. The scaling technique is applied to the Frank-Wolfe method, the partanized Frank-Wolfe method and a heuristic Frank-Wolfe method. The performance of  these algorithms with and without scaling is evaluated on the stochastic transportation problem. It is found that the scaling technique has the ability to improve the performance of some methods. In particular we observed a huge improvement in the performance of the partanized Frank-Wolfe method, especially when the scaling is used together with an exact line search and when the number of sets in the Cartesian product is large.
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Holmgren, Johan. "Efficient Updating Shortest Path Calculations for Traffic Assignment." Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2573.

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Traffic planning in a modern congested society is an important and time consuming procedure. Finding fast algorithms for solving traffic problems is therefore of great interest for traffic planners allover the world.

This thesis concerns solving the fixed demand traffic assignment problem (TAP) on a number of different transportation test networks. TAP is solved using the Frank-Wolfe algorithm and the shortest path problems that arise as subproblems to the Frank-Wolfe algorithm are solved using the network simplex algorithm. We evaluate how a number of existing pricing strategies to the network simplex algorithm performs with TAP. We also construct a new efficient pricing strategy, the Bucket Pricing Strategy, inspired by the heap implementation of Dijkstra's method for shortest path problems. This pricing strategy is, together with the actual use of the network simplex algorithm, the main result of the thesis and the pricing strategy is designed to take advantage of the special structure of TAP. In addition to performing tests on the conventional Frank-Wolfe algorithm, we also test how the different pricing strategies perform on Frank-Wolfe algorithms using conjugate and bi-conjugate search directions.

These test results show that the updating shortest path calculations obtained by using the network simplex outperforms the non-updating Frank-Wolfe algorithms. Comparisons with Bar-Gera's OBA show that our implementation, especially together with the bucket pricing strategy, also outperforms this algorithm for relative gaps down to 10E-6.

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Kerdreux, Thomas. "Accelerating conditional gradient methods." Thesis, Université Paris sciences et lettres, 2020. http://www.theses.fr/2020UPSLE002.

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Les algorithmes de Frank-Wolfe sont des méthodes d’optimisation de problèmes sous contraintes. Elles décomposent un problème non-linéaire en une série de problèmes linéaires. Cela en fait des méthodes de choix pour l’optimisation en grande dimension et notamment explique leur utilisation dans de nombreux domaines appliqués. Ici nous proposons de nouveaux algorithmes de Frank-Wolfe qui convergent plus rapidement vers la solution du problème d’optimisation sous certaines hypothèses structurelles assez génériques. Nous montrons en particulier, que contrairement à d’autres types d’algorithmes, cette famille s’adapte à ces hypothèses sans avoir à spécifier les paramètres qui les contrôlent
The Frank-Wolfe algorithms, a.k.a. conditional gradient algorithms, solve constrained optimization problems. They break down a non-linear problem into a series of linear minimization on the constraint set. This contributes to their recent revival in many applied domains, in particular those involving large-scale optimization problems. In this dissertation, we design or analyze versions of the Frank-Wolfe algorithms. We notably show that, contrary to other types of algorithms, this family is adaptive to a broad spectrum of structural assumptions, without the need to know and specify the parameters controlling these hypotheses
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Lindberg, Per Olov, and Maria Mitradjieva. "The Stiff is Moving - Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment." KTH, Transport- och lokaliseringsanalys, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-71400.

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We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, Conjugate direction Frank-Wolfe (CFW), Bi-conjugate Frank-Wolfe (BFW) and ”PARTANized” Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to Bar-Gera’s origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements suggested by Boyce et al. We further show that CFW is globally convergent. We moreover point at independent studies by other researchers that show that our methods compare favourably with recent bush-based and gradient projection algorithms on computers with several cores.

Updated from "E-publ" to published. QC 20130625

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Silveti, Falls Antonio. "First-order noneuclidean splitting methods for large-scale optimization : deterministic and stochastic algorithms." Thesis, Normandie, 2021. http://www.theses.fr/2021NORMC204.

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Dans ce travail, nous développons et examinons deux nouveaux algorithmes d'éclatement du premier ordre pour résoudre des problèmes d'optimisation composites à grande échelle dans des espaces à dimensions infinies. Ces problèmes sont au coeur de nombres de domaines scientifiques et d'ingénierie, en particulier la science des données et l'imagerie. Notre travail est axé sur l'assouplissement des hypothèses de régularité de Lipschitz généralement requises par les algorithmes de fractionnement du premier ordre en remplaçant l'énergie euclidienne par une divergence de Bregman. Ces développements permettent de résoudre des problèmes ayant une géométrie plus exotique que celle du cadre euclidien habituel. Un des algorithmes développés est l'hybridation de l'algorithme de gradient conditionnel, utilisant un oracle de minimisation linéaire à chaque itération, avec méthode du Lagrangien augmenté, permettant ainsi la prise en compte de contraintes affines. L'autre algorithme est un schéma d'éclatement primal-dual incorporant les divergences de Bregman pour le calcul des opérateurs proximaux associés. Pour ces deux algorithmes, nous montrons la convergence des valeurs Lagrangiennes, la convergence faible des itérés vers les solutions ainsi que les taux de convergence. En plus de ces nouveaux algorithmes déterministes, nous introduisons et étudions également leurs extensions stochastiques au travers d'un point de vue d'analyse de stablité aux perturbations. Nos résultats dans cette partie comprennent des résultats de convergence presque sûre pour les mêmes quantités que dans le cadre déterministe, avec des taux de convergence également. Enfin, nous abordons de nouveaux problèmes qui ne sont accessibles qu'à travers les hypothèses relâchées que nos algorithmes permettent. Nous démontrons l'efficacité numérique et illustrons nos résultats théoriques sur des problèmes comme la complétion de matrice parcimonieuse de rang faible, les problèmes inverses sur le simplexe, ou encore les problèmes inverses impliquant la distance de Wasserstein régularisée
In this work we develop and examine two novel first-order splitting algorithms for solving large-scale composite optimization problems in infinite-dimensional spaces. Such problems are ubiquitous in many areas of science and engineering, particularly in data science and imaging sciences. Our work is focused on relaxing the Lipschitz-smoothness assumptions generally required by first-order splitting algorithms by replacing the Euclidean energy with a Bregman divergence. These developments allow one to solve problems having more exotic geometry than that of the usual Euclidean setting. One algorithm is hybridization of the conditional gradient algorithm, making use of a linear minimization oracle at each iteration, with an augmented Lagrangian algorithm, allowing for affine constraints. The other algorithm is a primal-dual splitting algorithm incorporating Bregman divergences for computing the associated proximal operators. For both of these algorithms, our analysis shows convergence of the Lagrangian values, subsequential weak convergence of the iterates to solutions, and rates of convergence. In addition to these novel deterministic algorithms, we introduce and study also the stochastic extensions of these algorithms through a perturbation perspective. Our results in this part include almost sure convergence results for all the same quantities as in the deterministic setting, with rates as well. Finally, we tackle new problems that are only accessible through the relaxed assumptions our algorithms allow. We demonstrate numerical efficiency and verify our theoretical results on problems like low rank, sparse matrix completion, inverse problems on the simplex, and entropically regularized Wasserstein inverse problems
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Book chapters on the topic "Frank-Wolfe Method"

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Gass, Saul I., and Carl M. Harris. "Frank-Wolfe method." In Encyclopedia of Operations Research and Management Science, 314. New York, NY: Springer US, 2001. http://dx.doi.org/10.1007/1-4020-0611-x_366.

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Daneva, Maria, and Per Olov Lindberg. "A Conjugate Direction Frank-Wolfe Method with Applications to the Traffic Assignment Problem." In Operations Research Proceedings 2002, 133–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55537-4_21.

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"Frank-Wolfe Method." In Encyclopedia of Operations Research and Management Science, 609. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4419-1153-7_200246.

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Lambert, Tristan H. "C–O Ring Construction: The Martín and Martín Synthesis of Teurilene." In Organic Synthesis. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190646165.003.0043.

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Benjamin List at the Max-Planck-Institute in Mülheim reported (Angew. Chem. Int. Ed. 2013, 52, 3490) that the chiral phosphoric acid TRIP catalyzed the asymmet­ric SN2-type intramolecular etherification of 1 to produce tetrahydrofuran 2 with a selectivity factor of 82. The coupling of alkenol 3 with 4 to give the α-arylated tetra­hydropyran 5 via a method that combined gold catalysis and photoredox catalysis was disclosed (J. Am. Chem. Soc. 2013, 135, 5505) by Frank Glorius at Westfälische Wilhelms-Universität Münster. Mark Lautens at the University of Toronto reported (Org. Lett. 2013, 15, 1148) the conversion of cyclohexanedione 6 and phenylboronic acid to bicyclic ether 8 using rhodium catalysis in the presence of dienyl ligand 7. Propargylic ether 9 was found (Org. Lett. 2013, 15, 2926) by John P. Wolfe at the University of Michigan to undergo conversion to furanone 10 upon treatment with dibutylboron triflate and Hünig’s base followed by oxidation with hydrogen peroxide. Tomislav Rovis at Colorado State University demonstrated (Chem. Sci. 2013, 4, 1668) that the spirocyclic compound 13 could be prepared in enantioenriched form from 11 by a photoisomerization- coupled Stetter reaction using carbene catalyst 12. Antonio C. B. Burtoloso at the University of São Paulo reported (Org. Lett. 2013, 15, 2434) the conversion of ketone 14 to lactone 15 using samarium(II) iodide and methyl acrylate. The merger of diketone 16 and pyrone 17 in the presence of Amberlyst-15 to pro­duce (−)- tenuipyrone 18 was disclosed (Org. Lett. 2013, 15, 6) by Rongbiao Tong at the Hong Kong University of Science and Technology. Joanne E. Harvey at Victoria University of Wellington in New Zealand found (Org. Lett. 2013, 15, 2430) that tricy­clic ether 20 could be generated efficiently from dihydropyran 19 and pyrone 17 via a palladium-catalyzed double allylic alkylation cascade. Two rings and four stereocenters were generated in the construction of bicyclic ether 23 from dienol 21 and acetal 22 via a Lewis acid-mediated cascade, as reported (Org. Lett. 2013, 15, 2046) by Christine L. Willis at the University of Bristol.
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Conference papers on the topic "Frank-Wolfe Method"

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Cheung, Edward, and Yuying Li. "Projection Free Rank-Drop Steps." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/213.

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The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method for nuclear norm constrained problems. The goal is to generate descent steps that lead to rank decreases, maintaining low-rank solutions throughout the algorithm. Moreover, the optimization problems are constrained to ensure that the rank-drop step is also feasible and can be readily incorporated into a projection-free minimization method, e.g., Frank-Wolfe. We demonstrate that by incorporating rank-drop steps into the Frank-Wolfe algorithm, the rank of the solution is greatly reduced compared to the original Frank-Wolfe or its common variants.
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Gao, Hongchang, Hanzi Xu, and Slobodan Vucetic. "Sample Efficient Decentralized Stochastic Frank-Wolfe Methods for Continuous DR-Submodular Maximization." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/482.

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Continuous DR-submodular maximization is an important machine learning problem, which covers numerous popular applications. With the emergence of large-scale distributed data, developing efficient algorithms for the continuous DR-submodular maximization, such as the decentralized Frank-Wolfe method, became an important challenge. However, existing decentralized Frank-Wolfe methods for this kind of problem have the sample complexity of $\mathcal{O}(1/\epsilon^3)$, incurring a large computational overhead. In this paper, we propose two novel sample efficient decentralized Frank-Wolfe methods to address this challenge. Our theoretical results demonstrate that the sample complexity of the two proposed methods is $\mathcal{O}(1/\epsilon^2)$, which is better than $\mathcal{O}(1/\epsilon^3)$ of the existing methods. As far as we know, this is the first published result achieving such a favorable sample complexity. Extensive experimental results confirm the effectiveness of the proposed methods.
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Cheung, Edward, and Yuying Li. "Solving Separable Nonsmooth Problems Using Frank-Wolfe with Uniform Affine Approximations." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/281.

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Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to their ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the performance of the existing FW method hinges on the quality of the linear approximation. This typically restricts FW to smooth functions for which the approximation quality, indicated by a global curvature measure, is reasonably good. In this paper, we propose a modified FW algorithm amenable to nonsmooth functions, subject to a separability assumption, by optimizing for approximation quality over all affine functions, given a neighborhood of interest. We analyze theoretical properties of the proposed algorithm and demonstrate that it overcomes many issues associated with existing methods in the context of nonsmooth low-rank matrix estimation.
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Reddi, Sashank J., Suvrit Sra, Barnabas Poczos, and Alex Smola. "Stochastic Frank-Wolfe methods for nonconvex optimization." In 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2016. http://dx.doi.org/10.1109/allerton.2016.7852377.

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