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A Primal-Dual SGD Algorithm for Distributed Nonconvex Optimization [article]

Xinlei Yi, Shengjun Zhang, Tao Yang, Tianyou Chai, Karl H. Johansson
2022 arXiv   pre-print
We propose a distributed primaldual stochastic gradient descent (SGD) algorithm, suitable for arbitrarily connected communication networks and any smooth (possibly nonconvex) cost functions.  ...  The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.  ...  (i) We propose a distributed primal-dual SGD algorithm to solve the optimization problem (1).  ... 
arXiv:2006.03474v3 fatcat:4y2ajxafr5dmvewlcssa5iqwu4

Communication Efficient Primal-Dual Algorithm for Nonconvex Nonsmooth Distributed Optimization

Congliang Chen, Jiawei Zhang, Li Shen, Peilin Zhao, Zhi-Quan Luo
2021 International Conference on Artificial Intelligence and Statistics  
In this paper, we propose a distributed primal-dual algorithm to solve this type of problems in a decentralized manner and the proposed algorithm can achieve an O(1/ 2 ) iteration complexity to attain  ...  an -solution, which is the well-known lower iteration complexity bound for nonconvex optimization.  ...  Recently, some papers analyze the primal-dual algorithms for nonconvex cases.  ... 
dblp:conf/aistats/ChenZSZL21 fatcat:p3ogvbaorjbdho7chjx3bl3fry

Accelerated Primal-Dual Algorithm for Distributed Non-convex Optimization [article]

Shengjun Zhang, Colleen P. Bailey
2021 arXiv   pre-print
We propose a distributed primal-dual stochastic gradient descent (SGD) equipped with "powerball" method to accelerate.  ...  state-of-the-art distributed SGD algorithms and centralized SGD algorithms.  ...  Ye Yuan for their insightful inspirations and motivations on this work.  ... 
arXiv:2108.06050v3 fatcat:uafptmrbx5bnjlmjnez2mm4q7q

On the Convergence of A Family of Robust Losses for Stochastic Gradient Descent [article]

Bo Han and Ivor W. Tsang and Ling Chen
2016 arXiv   pre-print
To handle noisy labels, in this paper, we present a family of robust losses for SGD methods.  ...  However, vanilla SGD methods using convex losses cannot perform well with noisy labels, which adversely affect the update of the primal variable in SGD methods.  ...  For LIB-LINEAR, we set the bias b to 1 and the stopping tolerance ǫ to 10 −2 for primal solution and 10 −1 for dual solution by default.  ... 
arXiv:1605.01623v1 fatcat:hgssof3imfc6pkumwsm3x6ogia

A Nonlinear Bregman Primal-Dual Framework for Optimizing Nonconvex Infimal Convolutions [article]

Emanuel Laude, Daniel Cremers
2018 arXiv   pre-print
This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can  ...  We prove convergence of our scheme to stationary points of the original model for a specific choice of the penalty parameter.  ...  In (Condat, 2013) a primal-dual splitting algorithm is proposed for optimizing convex problems with inf-conv structure. In nonconvex optimization the Moreau-Envelope remains nonsmooth in general.  ... 
arXiv:1803.02487v2 fatcat:htyz64q435hgvffyk7rkwieltu

Distributed Stochastic Nonconvex Optimization and Learning based on Successive Convex Approximation [article]

Paolo Di Lorenzo, Simone Scardapane
2020 arXiv   pre-print
We introduce a novel algorithmic framework for the distributed minimization of the sum of the expected value of a smooth (possibly nonconvex) function (the agents' sum-utility) plus a convex (possibly  ...  We study distributed stochastic nonconvex optimization in multi-agent networks.  ...  The nonconvex and deterministic setting includes: i) primal gradient-based methods [11] ; ii) Frank-Wolfe algorithms [12] ; iii) SCA methods [13] ; proximal primal-dual algorithms [14] ; and distributed  ... 
arXiv:2004.14882v1 fatcat:oat7muwqzvfovjtx5atmmvna7m

Dual Free Adaptive Minibatch SDCA for Empirical Risk Minimization

Xi He, Rachael Tappenden, Martin Takáč
2018 Frontiers in Applied Mathematics and Statistics  
only allowed for a uniform selection of "dual" coordinates from a fixed probability distribution.  ...  In this paper we develop an adaptive dual free Stochastic Dual Coordinate Ascent (adfSDCA) algorithm for regularized empirical risk minimization problems.  ...  Stolyar for his insightful help with Algorithm 3. The material is based upon work supported by the U.S.  ... 
doi:10.3389/fams.2018.00033 fatcat:2yiednzs7vdjhgb75542rcsqfq

Convergence of Non-Convex Non-Concave GANs Using Sinkhorn Divergence

Risman Adnan, Muchlisin Adi Saputra, Junaidillah Fadlil, Martianus Frederic Ezerman, Muhamad Iqbal, Tjan Basaruddin
2021 IEEE Access  
There exists a primal-dual relationship π = exp ((f ⊕ g − c)/ε) · (µ θ ⊗ ν) (10) that links an OT plan to an optimal dual pair (f, g) that solves (8) . Proof.  ...  Strong duality and the primal-dual relationship hold for the dual problem. The proof comes from the 1 st order optimality conditions of the Fenchel-Rockafellar duality theorem [30, Prop. 3.5.6].  ...  He has a strong background in hardware programming and IoT and is keen on artificial intelligence.  ... 
doi:10.1109/access.2021.3074943 fatcat:mqtfhjhcyrgczdltztlwhiufre

Natural Policy Gradient Primal-Dual Method for Constrained Markov Decision Processes

Dongsheng Ding, Kaiqing Zhang, Tamer Basar, Mihailo R. Jovanovic
2020 Neural Information Processing Systems  
Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method for CMDPs which updates the primal variable via natural policy gradient ascent and the dual variable via projected sub-gradient  ...  To the best of our knowledge, our work is the first to establish non-asymptotic convergence guarantees of policybased primal-dual methods for solving infinite-horizon discounted CMDPs.  ...  In spite of the lack of convexity, our work provides global convergence guarantees for a new primal-dual algorithm without using any optimization oracles.  ... 
dblp:conf/nips/DingZBJ20 fatcat:fsr2qau7uvdfbj3fiu5g2pgrhy

DiNNO: Distributed Neural Network Optimization for Multi-Robot Collaborative Learning [article]

Javier Yu, Joseph A. Vincent, Mac Schwager
2021 arXiv   pre-print
We present a distributed algorithm that enables a group of robots to collaboratively optimize the parameters of a deep neural network model while communicating over a mesh network.  ...  We compare our algorithm to two existing distributed deep neural network training algorithms in (i) an MNIST image classification task, (ii) a multi-robot implicit mapping task, and (iii) a multi-robot  ...  The Choco-SGD algorithm for distributed deep learning [21] is another algorithm similar to DSGD with the variations that it uses a gossip mechanism for improved consensus, and incorporates a quantization  ... 
arXiv:2109.08665v1 fatcat:tfmyej6rmbgmzpv2fpkcfvg73i

Accelerated Zeroth-order Algorithm for Stochastic Distributed Nonconvex Optimization [article]

Shengjun Zhang, Colleen P. Bailey
2021 arXiv   pre-print
We propose a zeroth-order (ZO) distributed primal-dual stochastic coordinates algorithm equipped with "powerball" method to accelerate.  ...  We prove that the proposed algorithm has a convergence rate of 𝒪(√(p)/√(nT)) for general nonconvex cost functions.  ...  Yunlong Dong for their fruitful discussions on this work.  ... 
arXiv:2109.03224v2 fatcat:enu2sbqwuzcw5fbpuupumws4xu

Convergence Analysis of Nonconvex Distributed Stochastic Zeroth-order Coordinate Method [article]

Shengjun Zhang, Yunlong Dong, Dong Xie, Lisha Yao, Colleen P. Bailey, Shengli Fu
2021 arXiv   pre-print
In this paper, we propose a ZO distributed primal-dual coordinate method (ZODIAC) to solve the stochastic optimization problem.  ...  This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of n local cost functions.  ...  Xinlei Yi for his insightful inspirations and motivations on this work.  ... 
arXiv:2103.12954v4 fatcat:a63gdmvicjddfhwzt3hmus2nh4

Deep Neural Networks with Multi-Branch Architectures Are Intrinsically Less Non-Convex

Hongyang Zhang, Junru Shao, Ruslan Salakhutdinov
2019 International Conference on Artificial Intelligence and Statistics  
Our two results work for arbitrary depths, while the analytical techniques might be of independent interest to non-convex optimization more broadly.  ...  For the neural networks with arbitrary activation functions, multi-branch architecture and a variant of hinge loss, we show that the duality gap of both population and empirical risks shrinks to zero as  ...  There are two reasons for such an argument. a) The optimal value of the dual problem is equal to the optimal value of the convex relaxation of the primal problem.  ... 
dblp:conf/aistats/ZhangSS19 fatcat:xqyj73xuxvfk5m2bxvlr4zwiba

Variance Reduced Policy Evaluation with Smooth Function Approximation

Hoi-To Wai, Mingyi Hong, Zhuoran Yang, Zhaoran Wang, Kexin Tang
2019 Neural Information Processing Systems  
We formulate the policy evaluation problem as a non-convex primal-dual, finite-sum optimization problem, whose primal sub-problem is non-convex and dual sub-problem is strongly concave.  ...  We suggest a single-timescale primal-dual gradient algorithm with variance reduction, and show that it converges to an �-stationary point using O(m/�) calls (in expectation) to a gradient oracle.  ...  We propose the Nonconvex Primal-Dual Gradient with Variance Reduction (nPD-VR) algorithm for (16) in Algorithm 1.  ... 
dblp:conf/nips/WaiHYWT19 fatcat:ndjfntbsazgbvpq7hueon65544

Zeroth Order Nonconvex Multi-Agent Optimization over Networks [article]

Davood Hajinezhad, Mingyi Hong, Alfredo Garcia
2019 arXiv   pre-print
Differently from all existing works on distributed optimization, our focus is given to optimizing a class of non-convex problems, and under the challenging setting where each agent can only access the  ...  For different types of network topologies such as undirected connected networks or star networks, we develop efficient distributed algorithms and rigorously analyze their convergence and rate of convergence  ...  In [20, 24] a primal-dual based algorithm with provable convergence rate have been designed for distributed nonconvex optimization problem.  ... 
arXiv:1710.09997v3 fatcat:epyt6lusujaelkyjbm77m5iqmm
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