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Asynchronous Stochastic Frank-Wolfe Algorithms for Non-Convex Optimization

Bin Gu, Wenhan Xian, Heng Huang
2019 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence  
However, our understanding of asynchronous stochastic Frank-Wolfe algorithms is extremely limited especially in the non-convex setting.  ...  To address this challenging problem, in this paper, we propose our asynchronous stochastic Frank-Wolfe algorithm (AsySFW) and its variance reduction version (AsySVFW) for solving the constrained non-convex  ...  As far as we know, the convergence guarantee of asynchronous stochastic Frank-Wolfe algorithms for solving the constrained non-convex optimization problem (1) is still an open question.  ... 
doi:10.24963/ijcai.2019/104 dblp:conf/ijcai/GuXH19 fatcat:y2fccqpyqzhnfc2hqqdelh3fte

Communication-Efficient Asynchronous Stochastic Frank-Wolfe over Nuclear-norm Balls [article]

Jiacheng Zhuo, Qi Lei, Alexandros G. Dimakis, Constantine Caramanis
2019 arXiv   pre-print
In this work, we propose an asynchronous Stochastic Frank Wolfe (SFW-asyn) method, which, for the first time, solves the two problems simultaneously, while successfully maintaining the same convergence  ...  We implement our algorithm in python (with MPI) to run on Amazon EC2, and demonstrate that SFW-asyn yields speed-ups almost linear to the number of machines compared to the vanilla SFW.  ...  We propose a Stochastic Frank-Wolfe algorithm (SFW-asyn) that is communication-efficient and runs asynchronously.  ... 
arXiv:1910.07703v1 fatcat:kaxmvnegunak3lr2l7smmnglzi

D-FW: Communication efficient distributed algorithms for high-dimensional sparse optimization

Jean Lafond, Hoi-To Wai, Eric Moulines
2016 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
D-FW: Communication Efficient Distributed Algorithms 4 / 20 Agenda 1 Frank-Wolfe algorithm Recent results on stochastic FW 2 Distributed FW algorithms for sparse optimization DistFW algorithm for star  ...  networks DeFW algorithm for general networks Convergence Analysis 3 Numerical Experiment 4 Conclusions & Future Work D-FW: Communication Efficient Distributed Algorithms 5 / 20 Frank-Wolfe (FW) algorithm  ...  Veeravalli, "Distributed Stochastic Subgradient Projection Algorithms for Convex Optimization," J. Optim. Theory. Appl., Dec., 2010.  ... 
doi:10.1109/icassp.2016.7472457 dblp:conf/icassp/LafondWM16 fatcat:2ddxosmbhnhspg3xmzkxzb3p3y

On Connections between Constrained Optimization and Reinforcement Learning [article]

Nino Vieillard, Olivier Pietquin, Matthieu Geist
2019 arXiv   pre-print
In this paper, we draw connections between DP and (constrained) convex optimization.  ...  We link Conservative Policy Iteration to Frank-Wolfe, Mirror-Descent Modified Policy Iteration to Mirror Descent, and Politex (Policy Iteration Using Expert Prediction) to Dual Averaging.  ...  Many RL algorithms can be seen as approximate and possibly asynchronous and stochastic variations of DP algorithms, mainly PI and VI.  ... 
arXiv:1910.08476v2 fatcat:n3ajeezfcvgghnztbonzstukzy

Modified Frank Wolfe in Probability Space

Carson Kent, Jiajin Li, José H. Blanchet, Peter W. Glynn
2021 Neural Information Processing Systems  
We propose a novel Frank-Wolfe (FW) procedure for the optimization of infinitedimensional functionals of probability measures -a task which arises naturally in a wide range of areas including statistical  ...  be efficiently computed using finite-dimensional, convex optimization methods.  ...  an infinite-dimensional Frank-Wolfe algorithm.  ... 
dblp:conf/nips/KentLBG21 fatcat:ve5fzqncfre4fmoueeukw2rpq4

Communication-Efficient Projection-Free Algorithm for Distributed Optimization [article]

Yan Li, Chao Qu, Huan Xu
2018 arXiv   pre-print
Compared to the state-of-the-art distributed Frank-Wolfe algorithm, our algorithm attains the same communication complexity under much more realistic assumptions.  ...  In contrast to the consensus based algorithm, DCGS is based on the primal-dual algorithm, yielding a modular analysis that can be exploited to improve linear oracle complexity whenever centralized Frank-Wolfe  ...  Communication-Efficient Algorithms for Decentralized and Stochastic Optimization. ArXiv e-prints. Lan, G., Zhou, Y., 2016. Conditional gradient sliding for convex optimization.  ... 
arXiv:1805.07841v1 fatcat:5zd2xutccja4rcmhmaolnrae44

A Unified q-Memorization Framework for Asynchronous Stochastic Optimization

Bin Gu, Wenhan Xian, Zhouyuan Huo, Cheng Deng, Heng Huang
2020 Journal of machine learning research  
Specifically, based on the q-memorization framework, 1) we propose an asynchronous stochastic gradient hard thresholding algorithm with q-memorization (AsySGHT-qM) for the non-convex optimization with  ...  proximal gradient algorithm (AsySPG-qM) for the convex optimization with non-smooth regularization, and prove that AsySPG-qM can achieve a linear convergence rate. 3) We propose an asynchronous stochastic  ...  Gu et al. (2019) proposed asynchronous stochastic Frank-Wolfe algorithm and its SVRG variant, and proved their convergence rates.  ... 
dblp:journals/jmlr/GuXHDH20 fatcat:6mqu7l6jz5gtjkmrux5qihhoxu

Fully Projection-free Proximal Stochastic Gradient Method with Optimal Convergence Rates

Yan Li, Xiaofeng Cao, Honghui Chen
2020 IEEE Access  
To reduce complexity, many projection-free methods such as Frank-Wolfe methods have been proposed.  ...  Our theoretical analysis shows that the proposed method achieves convergence rates of O 1 √ T and O log T T for convex and strongly convex functions, respectively.  ...  The conditional gradient descent (a.k.a Frank-Wolfe algorithm) was originally proposed by Frank and Wolfe [9] for offline smooth optimization over polyhedral sets.  ... 
doi:10.1109/access.2020.3019885 fatcat:biauxqkujral7es2yws2hjp7ou

Convex Optimization for Big Data: Scalable, randomized, and parallel algorithms for big data analytics

Volkan Cevher, Stephen Becker, Mark Schmidt
2014 IEEE Signal Processing Magazine  
This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks.  ...  The new Big Data algorithms are based on surprisingly simple principles and attain staggering accelerations even on classical problems.  ...  When g represents the indicator function of a compact set, the Frank-Wolfe method solves (9) without the quadratic term and can achieve an O(1/ ) convergence rate in the convex case [16] .  ... 
doi:10.1109/msp.2014.2329397 fatcat:7np3knuhena2fd5o6tqjtpbzai

A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning [chapter]

Aurélien Bellet, Yingyu Liang, Alireza Bagheri Garakani, Maria-Florina Balcan, Fei Sha
2015 Proceedings of the 2015 SIAM International Conference on Data Mining  
We address the key challenges of balancing communication costs and optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW) algorithm.  ...  We obtain theoretical guarantees on the optimization error and communication cost that do not depend on the total number of combining elements.  ...  Acknowledgments Computation for the work described in this paper was supported by the University of Southern California's Center for High-Performance Computing (http://hpcc.usc.edu).  ... 
doi:10.1137/1.9781611974010.54 dblp:conf/sdm/BelletLGBS15 fatcat:iokm4j2t3nak7g3v3qcwo3woee

Byzantine Fault Tolerance in Distributed Machine Learning : a Survey [article]

Djamila Bouhata, Hamouma Moumen
2022 arXiv   pre-print
Mainly in first-order optimization methods, especially Stochastic Gradient Descent (SGD). We highlight the key techniques as well as fundamental approaches.  ...  This classification is established on specific criteria such as communication process, optimization method, and topology setting, which characterize future work methods examining the current challenges  ...  The authors prove the statistical error rates for the three types of population loss functions (strongly convex, non-strongly convex, and non-convex) and the algorithms' robustness against Byzantine failures  ... 
arXiv:2205.02572v1 fatcat:h2hkcgz3w5cvrnro6whl2rpvby

Parallel and Distributed Block-Coordinate Frank-Wolfe Algorithms [article]

Yu-Xiang Wang and Veeranjaneyulu Sadhanala and Wei Dai and Willie Neiswanger and Suvrit Sra and Eric P. Xing
2016 arXiv   pre-print
Our algorithms assume block-separable constraints, and subsume the recent Block-Coordinate Frank-Wolfe (BCFW) method lacoste2013block.  ...  We develop parallel and distributed Frank-Wolfe algorithms; the former on shared memory machines with mini-batching, and the latter in a delayed update framework.  ...  We propose the first asynchronous algorithm for Frank-Wolfe.  ... 
arXiv:1409.6086v2 fatcat:qtf4bgwoqnawlhg3xyuivhixe4

Projection-free Decentralized Online Learning for Submodular Maximization over Time-Varying Networks

Junlong Zhu, Qingtao Wu, Mingchuan Zhang, Ruijuan Zheng, Keqin Li
2021 Journal of machine learning research  
In addition, we also propose a decentralized one-shot Frank-Wolfe online learning method in the stochastic online setting.  ...  To address the problem, we propose a decentralized Meta-Frank-Wolfe online learning method in the adversarial online setting by using local communication and local computation.  ...  Acknowledgments We would like to acknowledge support for this project in part by the National Natural Science Foundation of China (NSFC) under Grants no. 61976243, and no. 61971458  ... 
dblp:journals/jmlr/ZhuWZZL21 fatcat:bxfjfgat2rdvtexks2cwzsriqi

A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning [article]

Aurélien Bellet, Yingyu Liang, Alireza Bagheri Garakani, Maria-Florina Balcan, Fei Sha
2015 arXiv   pre-print
We address the key challenges of balancing communication costs and optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW) algorithm.  ...  We obtain theoretical guarantees on the optimization error ϵ and communication cost that do not depend on the total number of combining elements.  ...  Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon.  ... 
arXiv:1404.2644v3 fatcat:5it5qte545gftpflpifrap53ea

Escaping from Zero Gradient: Revisiting Action-Constrained Reinforcement Learning via Frank-Wolfe Policy Optimization [article]

Jyun-Li Lin, Wei Hung, Shang-Hsuan Yang, Ping-Chun Hsieh, Xi Liu
2021 arXiv   pre-print
To tackle this issue, we propose a learning algorithm that decouples the action constraints from the policy parameter update by leveraging state-wise Frank-Wolfe and a regression-based policy update scheme  ...  Moreover, we show that the proposed algorithm enjoys convergence and policy improvement properties in the tabular case as well as generalizes the popular DDPG algorithm for action-constrained RL in the  ...  Convergence rate of Frank-Wolfe for non-convex objectives. arXiv:1607.00345, 2016.  ... 
arXiv:2102.11055v2 fatcat:rszg6evqr5dqjfhrb5ztxekxna
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