�0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� The link between communication complexity and nonnegative rank was also instrumental recently in proving exponential lower bounds on the sizes of extended formulations of the Traveling Salesman polytope, answering a longstanding open problem. Communication Complexity of Convex Optimization* JOHN N. TSITSIKLIS AND ZHI-QUAN Luo Laboratory for Information and Decision Systems and the Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 We consider a situation where each of two processors has access to a different convex functionA, i = 1,2, defined on a common bounded domain. <>>>/BBox[0 0 612 792]/Length 164>>stream x�ν x�ν The tutorial contains two parts. <>stream endobj We first resolve the randomized and deterministic communication complexity in the point-to-point model of communication, showing it is $\tilde{\Theta}(d^2L + sd)$ and $\tilde{\Theta}(sd^2L)$, respectively. We start with the problem of solving a linear system. The processors are to exchange a number of binary messages, according to some protocol, until they find a point in the domain at which f1+f2 is minimized, within some prespecified accuracy ?. 55 0 obj endstream endobj x�S�*�*T0T0 B�kh�g������i������ ��� endstream endobj We start with the problem of solving a linear system. Basic tests on the optimization of all-to-all communication and stencil communication were carried out on … endstream 06/05/2015 ∙ by Yossi Arjevani, et al. When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. Agreement NNX16AC86A, Is ADS down? 8 0 obj <>>>/BBox[0 0 612 792]/Length 164>>stream <>stream 30 Scopus citations. We start with the problem of solving a linear system. x�+� � | Home Conferences NIPS Proceedings NIPS'15 Communication complexity of distributed convex learning and optimization. �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� <>stream <>>>/BBox[0 0 612 792]/Length 164>>stream endobj x�S�*�*T0T0 B�kh�g������ih������ ��! 23 0 obj Our second … The pheromone-based communication of biological ants is often the predominant paradigm used. x�S�*�*T0T0 B�kh�g������ih������ �� x�S�*�*T0T0 B�kh�g������i������ ��� In particular we will discuss (statistical) learning theory, (deep) neural networks, first order optimization methods such as stochastic gradient descent and their analysis, the interplay of learning and optimization, empirical risk minimization and regularization, and modern views of machine learning in the overparameterized regime with deep neural networks. q 124 0 obj 9 0 obj Laboratory for Information and Decision Systems. 3 0 obj endobj convex optimization with O(1= p NT) computation com-plexity and O(p TNlog(T N)) communication complexity. endstream endobj <>stream <>stream The Communication Complexity of Optimization 123 0 obj endstream We consider the communication complexity of a number of distributed optimization problems. solve linear optimization problems on F in polynomial time using any of the polynomial-time LP solvers. endobj endstream endstream x�+� � | x�+� � | endobj For general and in the point-to-point model, we show an upper bound and an lower bound. x�+� � | endstream endstream Towards this end, we consider the communication complexity of optimization tasks which generalize linear systems. 41 0 obj endstream endobj 21 0 obj endobj ∙ Weizmann Institute of Science ∙ 0 ∙ share . Browse SIFIN; SIAM J. on Imaging Sciences. 2018), and the communication complexity matches the ex-isting communication lower bound (Sun & Hong, 2019) for decentralized non-convex optimization (in terms of the de-pendency in ). <>stream COMMUNICATION COMPLEXITY OF CONVEX OPTIMIZATION. endstream While this problem has been studied, we give improved upper or lower bounds for every value of $p \ge 1$. Santosh S. Vempala, Ruosong Wang and David P. Woodruff endobj The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Browse SIMA; SIAM J. on Mathematics of Data Science. endobj Part of: Advances in Neural Information Processing Systems 28 (NIPS 2015) A note about reviews: "heavy" review comments were provided by reviewers in the program committee as part of the evaluation process for NIPS 2015, along with posted responses during the author feedback period. This method maximizes the throughput of the D2D system and guarantees the minimum rate per user. endstream Share on. An extension of the well-known Particle Swarm Optimization (PSO) to multi-robot applications has been recently proposed and denoted as Robotic Darwinian PSO (RDPSO), benefited from the dynamical partitioning of the whole population of robots. <>>>/BBox[0 0 612 792]/Length 164>>stream The problem is usually stated as … <>>>/BBox[0 0 612 792]/Length 164>>stream We assume each coefficient of each constraint is specified using $L$ bits. x�S�*�*T0T0 B�kh�g������i������ ��� as limited communication in distributed settings [4], may signiﬁcantly affect the overall runtime). Communication Complexity of Dual Decomposition Methods for Distributed Resource Allocation Optimization Abstract: Dual decomposition methods are among the most prominent approaches for finding primal/dual saddle point solutions of resource allocation optimization problems. If we pause for just a moment to consider the sheer number of situational possibilities before an agent greets a customer, the complexity is staggering. endobj For general $d$ and in the point-to-point model, we show an $\tilde{O}(sd^3 L)$ upper bound and an $\tilde{\Omega}(d^2 L + sd)$ lower bound. For linear programming, we first resolve the communication complexity when $d$ is constant, showing it is $\tilde{\Theta}(sL)$ in the point-to-point model. x�ν endobj Electrical and Computer Engineering; Research output: Contribution to journal › Article. endobj We consider a situation where each of two processors has access to a different convex function φ i, i = 1, 2, defined on a common bounded domain. 60 0 obj <>stream 1 0 obj 2018), and the communication complexity matches the ex-isting communication lower bound (Sun & Hong, 2019) for decentralized non-convex optimization (in terms of the de-pendency in ). We obtain similar results for the blackboard model. x�ν The communication complexity of optimization. <>>>/BBox[0 0 612 792]/Length 164>>stream The classical data-parallel implementation of SGD over N workers can achieve linear speedup … <>stream 45 0 obj Get the latest machine learning methods with code. Research output: Contribution to journal › Conference article. <>stream 24 0 obj endstream Abstract. endstream endobj The link between communication complexity and nonnegative rank was also instrumental recently in proving exponential lower bounds on the sizes of extended formulations of the Traveling Salesman polytope, answering a longstanding open problem. 62 0 obj 59 0 obj endobj communication complexity is defined to be the minimum number of messages that has to be exchanged between the processors in order to exactly evaluate f(x, y). 39 0 obj ; Massachusetts Institute of Technology. On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation We first resolve the randomized and deterministic communication complexity in the point-to-point model of communication, showing it is $\tilde{\Theta}(d^2L + sd)$ and $\tilde{\Theta}(sd^2L)$, respectively. endstream <>stream We consider the communication complexity of a number of distributed optimization problems. We obtain similar results for the blackboard model. We consider a situation where each one of two processors has access to a different convex function fi, i = 1, 2, defined on a common bounded domain. x�ν 44 0 obj endobj <>stream The values of each function are assumed to reside at a different memory element. x�ν endstream Request PDF | The Communication Complexity of Optimization | We consider the communication complexity of a number of distributed optimization problems. 57 0 obj Browse SIMODS; SIAM J. on Matrix Analysis and Applications. <>stream <>>>/BBox[0 0 612 792]/Length 164>>stream <>>>/BBox[0 0 612 792]/Length 164>>stream The p… <>stream endobj We start with the problem of solving a linear system. Perhaps the most closely-related paper is [22], which studied the communication complexity of distributed opti-mization, and showed that Ω(dlog(1/ǫ)) bits of communication are necessary between the machines, for d-dimensional convex problems. <>stream We identify cases where existing algorithms are already worst-case optimal, as well as cases where room for further improvement is still possible. This seminar brought together researchers from Matrix Theory, Combinatorial Optimization, and Communication Complexity to promote the transfer of … �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� 15 0 obj We also show if one perturbs the coefficients randomly by numbers as small as $2^{-\Theta(L)}$, then the upper bound is $\tilde{O}(sd^2 L) + \textrm{poly}(dL)$. … In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem is distributed among two or more parties. Communication Complexity of Distributed Convex Learning and Optimization. x�ν For general $d$ and in the point-to-point model, we show an $\tilde{O}(sd^3 L)$ upper bound and an $\tilde{\Omega}(d^2 L + sd)$ … 38 0 obj <>>>/BBox[0 0 612 792]/Length 164>>stream endstream 46 0 obj Communication complexity of convex optimization Abstract: We consider a situation where each one of two processors has access to a different convex function fi, i = 1, 2, defined on a common bounded domain. When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. x�S�*�*T0T0 B�kh�g������i������ ��� �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� endstream endobj x�+� � | x�+� � | x�+� � | <>stream pdfTeX-1.40.19; modified using iText 4.2.0 by 1T3XT View Profile, Ruosong Wang. x�S�*�*T0T0 B�kh�g������ih������ �� x�+� � | Georgia Tech. Computer Science - Data Structures and Algorithms. Allow me the liberty to be painfully specific. Browse SIMAX 52 0 obj 17 0 obj x�S�*�*T0T0 B�kh�g������i������ ��� On the Computation and Communication Complexity of Parallel SGD with Dynamic Batch Sizes for Stochastic Non-Convex Optimization Hao Yu 1Rong Jin Abstract For SGD based distributed stochastic optimiza- tion, computation complexity, measured by the convergence rate in terms of the number of stochasticgradientcalls,andcommunicationcom-plexity, measured by the number of inter-node communication … We obtain similar results for the blackboard model. 13 0 obj Request PDF | On Jan 1, 2020, Santosh S. Vempala and others published The Communication Complexity of Optimization | Find, read and cite all the research you need on ResearchGate <>>>/BBox[0 0 612 792]/Length 164>>stream endobj endstream 10 0 obj When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� Furthermore, the proposed approach is also able to achieve O(m 3/2) sample complexity and O( 1) communication complexity for the online problem (3), re- x�S�*�*T0T0 B�kd�g������i������ ��� x�ν However, in our setting this does not endobj SIAM J. on Control and Optimization. Contributions. 2019-10-30T22:42:01-04:00 The algorithm isn't practical due to the communication cost inherent in moving data to and from the temporary matrix T, but a more practical variant achieves Θ(n 2) speedup, without using a temporary matrix. x�S�*�*T0T0 B�kh�g������i������ ��� endstream endobj <>>>/BBox[0 0 612 792]/Length 164>>stream endobj We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees. Communication Complexity of Dual Decomposition Methods for Distributed Resource Allocation Optimization Sindri Magnusson, Chinwendu Enyioha, Na Li, Carlo Fischione, and Vahid Tarokh´ Abstract— Dual decomposition methods are among the most prominent approaches for ﬁnding primal/dual saddle point so-lutions of resource allocation optimization problems. <>>>/BBox[0 0 612 792]/Length 164>>stream Browse SIDMA; SIAM J. on Financial Mathematics. <>stream Block matrix multiplication. For linear programming, we first resolve the communication complexity when $d$ is constant, showing it is $\tilde{\Theta}(sL)$ in the point-to-point model. 50 0 obj �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation Author links open overlay panel Mehran Mesbahi a 1 … endstream <>stream We study the fundamental limits to communication-efficient distributed methods for convex learning and optimization, under different assumptions on the information available to individual machines, and the types of functions considered. 16 0 obj <>stream Tsitsiklis, JN & Luo, ZQ 1986, ' COMMUNICATION COMPLEXITY OF CONVEX OPTIMIZATION. 25 0 obj uuid:ad063bcd-7e30-4df5-b370-1e5fbd92bca4 Authors: Santosh S. Vempala. x�S�*�*T0T0 B�kh�g������ih������ �� endobj Author(s) Tsitsiklis, John N.; Luo, Zhi-Quan. 06/13/2019 ∙ by Santosh S. Vempala, et al. We first resolve the randomized and deterministic communication complexity in the point-to-point model of communication, showing it is $\tilde{\Theta}(d^2L + sd)$ and $\tilde{\Theta}(sd^2L)$, respectively. <>stream �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� endstream Suppose there is a coordinator together with sservers P 1;:::;P s, the i-th �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� Get the latest machine learning methods with code. This paper introduces a measure of communication complexity for a two-agent distributed control system where controls are subject to finite bandwidth communication constraints. 61 0 obj 6 0 obj 2020-12-14T03:28:12-08:00 Notice, Smithsonian Terms of However, it remains unclear whether any distributed momentum SGD possesses the … <>stream One takeaway message is that sampling and sketching techniques, which are commonly used in earlier work on distributed optimization, are neither optimal in the dependence on $d$ nor on the dependence on the approximation $\epsilon$, thus motivating new techniques from optimization to solve these problems. We obtain similar results for the blackboard model. endstream x�S�*�*T0T0 B�kh�g������ih������ �� We show that our first method is optimal both in terms of the number of communication rounds and in terms of the number of gradient computations. endstream endstream 42 0 obj <>>>/BBox[0 0 612 792]/Length 164>>stream Despite my many years as both a Professor of Communication and consultant for the Call Center Industry, I am still amazed by the complexity of human communication. <>>>/BBox[0 0 612 792]/Length 164>>stream We believe that these issues yield new and interest-ing questions in multi-player communication complexity. �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� endobj x�+� � | communication complexity (as in (Nemirovski et al., 2009; Bottou et al., 2018)) is missing for stochastic non-convex optimization. endstream q Browse our catalogue of tasks and access state-of-the-art solutions. endobj 18 0 obj x�+� � | This work analyses different communication modes in applications of supercomputing, proposes a communication dynamic performance model based on topology awareness, and realizes the prototype system of all-to-all communication and stencil communication optimization based on this model. application/pdf endobj endstream endstream endstream Share on. endobj x�+� � | 56 0 obj View Profile, Ohad Shamir. <>stream uuid:307fdd91-9ba4-41e4-b60a-f82c75d6209e The … We consider a situation where each of two processors has access to a different convex function φi, i = 1, 2, defined on a common bounded domain. We consider the problem of approximating the maximum of the sum of m Lipschitz continuous functions. <>stream When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. ∙ 0 ∙ share We consider the communication complexity of a number of distributed optimization problems. endstream We consider the communication complexity of a number of distributed optimization problems. Browse SICON; SIAM J. on Discrete Mathematics. Perhaps the most closely-related paper is [22], which studied the communication complexity of distributed optimization, and showed that (dlog(1= )) bits of communication are necessary between the machines, for d-dimensional convex problems. 2020-12-14T03:28:12-08:00 x�S�*�*T0T0 B�kh�g������i������ ��� 35 0 obj Towards this end, we consider the communication complexity of optimization tasks which generalize linear systems. x�+� � | endobj x�ν and optimization, but to the best of our knowledge, none of them provide a similar type of results. <>>>/BBox[0 0 612 792]/Length 164>>stream endobj endstream A single processing element is … The Communication Complexity of Optimization. �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� 4 0 obj 5 0 obj Suppose there is a coordinator together with $s$ servers $P_1, \ldots, P_s$, the $i$-th of which holds a subset $A^{(i)} x = b^{(i)}$ of $n_i$ constraints of a linear system in $d$ variables, and the coordinator would like to output $x \in \mathbb{R}^d$ for which $A^{(i)} x = b^{(i)}$ for $i = 1, \ldots, s$. endstream 32 0 obj We consider the communication complexity of a number of distributed optimization problems. Communication Complexity of Dual Decomposition Methods for Distributed Resource Allocation Optimization Abstract: Dual decomposition methods are among the most prominent approaches for finding primal/dual saddle point solutions of resource allocation optimization problems. x�+� � | Furthermore, the proposed approach is also able to achieve O(m 3/2) sample complexity and O( 1) communication complexity for the online problem (3), re- Weizmann Institute of Science, Rehovot, Israel . x�S�*�*T0T0 B�kh�g������ih������ �y �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� endobj Use, Smithsonian ', Proceedings of the IEEE Conference on Decision and … Communication Complexity of Distributed Convex Learning and Optimization. An Introduction to Convex Optimization for Communications and Signal Processing Zhi -Quan Luo, Senior Member, IEEE, and Wei Yu, Member, IEEE Tutorial Paper Abstract—Convex optimization methods are widely used in the design and analysis of communication systems and signal pro-cessing algorithms. This tutorial surveys some of recent progress in this area. Browse SIIMS; SIAM J. on Mathematical Analysis. 122 0 obj endobj <>stream �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� ; Massachusetts Institute of Technology. x�S�*�*T0T0 B�kh�g������ih������ �� Speciﬁcally, the training data is distributed among Mworkers and each … False <>>>/BBox[0 0 612 792]/Length 164>>stream <>stream endstream endstream 27 0 obj <>stream <>stream %���� <>stream endstream endstream We identify cases where existing algorithms are already worst-case optimal, as well as cases where room for further improvement is still possible. endobj �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� x�ν endstream This seminar brought together researchers from Matrix Theory, Combinatorial Optimization, and Communication Complexity to promote the transfer of … Communication Complexity of Distributed Convex Learning and Optimization. 30 0 obj <>>>/BBox[0 0 612 792]/Length 164>>stream endstream endstream / Tsitsiklis, John N.; Luo, Zhi Quan. Browse our catalogue of tasks and access state-of-the-art solutions. endobj LaTeX with hyperref endstream John N. Tsitsiklis, Zhi Quan Luo. endstream �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� Finite-Rank ADI Iteration for Operator Lyapunov Equations Diffraction Coefficients for Higher Order Edges and Vertices 37 0 obj x�S�*�*T0T0 B�kh�g������i������ ��� Bibliography: leaf 10. 51 0 obj 11 0 obj endstream Astrophysical Observatory. 19 0 obj endobj 28 0 obj endstream <>stream �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� 49 0 obj 7 0 obj endobj x�S�*�*T0T0 B�kh�g������i������ ��� H��WK������Q
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�M6�M4���¶�na$ˑ�~�O��, Santosh S. Vempala, Ruosong Wang and David P. Woodruff, The Communication Complexity of Optimization. Authors: Yossi Arjevani. The study of communication complexity was first introduced by Andrew Yao in 1979, while studying the problem of computation distributed among several machines. <>stream %PDF-1.5 However, these papers do not study algorithm invariant quantities such as communication complexity. No code available yet. x�ν endobj endobj endstream 48 0 obj endobj communication complexity, quantum communication complexity, quantum information theory, set-disjointness, the log-rank conjecture in communication complexity AMS Subject Headings 68M10 , … endobj endstream 40 0 obj <>stream <>stream 12 0 obj endstream 26 0 obj endstream endstream endobj 54 0 obj endstream Georgia Tech. endobj The reduced communication complexity is desirable since communication overhead is often the performance bottleneck in distributed systems. x�ν x�+� � | We consider the problem of approximating the maximum of the sum of m Lipschitz continuous functions. For linear programming, we first resolve the communication complexity when is constant, showing it is in the point-to-point model. Part of Advances in Neural Information Processing Systems 28 (NIPS 2015) Bibtex » Metadata » Paper » Reviews » Supplemental » Authors. 36 0 obj 20 0 obj endobj 29 0 obj <>stream The data parallel mechanism is a widely used architecture for distributed optimization, which has received much recent attention due to data explosion and increasing model complexity. 58 0 obj <>stream endstream <>stream In: Proceedings of the IEEE Conference on Decision and Control, 01.12.1986, p. 608-611. endstream 43 0 obj <>>>/BBox[0 0 612 792]/Length 164>>stream 53 0 obj <>>>/BBox[0 0 612 792]/Length 164>>stream However, in our setting thisdoes not lead to any non … Bibliography: leaf 10. We start with the problem of solving a linear system. x�+� � | <>stream 31 0 obj x�ν x�+� � | On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation . <>stream Title: The Communication Complexity of Optimization Authors: Santosh S. Vempala , Ruosong Wang , David P. Woodruff (Submitted on 13 Jun 2019 ( … �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� Unlike existing optimal algorithms, our algorithm does not rely on the expensive evaluation of dual gradients. <>stream <>stream Weizmann Institute of Science, Rehovot, Israel. endobj In both cases, using dynamic batch sizes can achieve the linear speedup of convergence with communication com-plexity less than that of existing communication efﬁcient parallel SGD methods with ﬁxed batch sizes (Stich,2018; Yu et al.,2018). endobj Author(s) Tsitsiklis, John N.; Luo, Zhi-Quan. In , the resource allocation problem in the underlying cellular network of D2D communication was defined as a game of alliance formation, and the power allocation was optimized by the whale optimization algorithm (WOA). x�S�*�*T0T0 B�kh�g������ih������ �� x�ν Laboratory for Information and Decision Systems. x�S�*�*T0T0 B�kh�g������ih������ �� endstream x�ν Towards this end, we consider the communication complexity of optimization tasks which generalize linear systems. Methods such as the ellipsoid algorithm have shown that linear programming is solvable in polynomial time. Besides the work in [20], communication complexity of dis-tributed optimization problems has not received much attention in the literature. (or is it just me...), Smithsonian Privacy x�ν CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): . endstream endobj endobj endobj <>stream x�ν <>stream �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� x�ν �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� <>stream �0��=WqFLrj,��������slS�&䤈w�Y>x���ꆀ�[h@� 蜸5�,�Nbu�y�UK-`�ШBC�`vrWʽ�X Oj���%9?/�@Mʿ����543����������������,�U���S��H%��� 2*���IW+~vo5� endobj endobj endstream Recently, momentum methods are more and more widely adopted by practitioners to train machine learning models since they can often converge faster and generalize better. endobj <>stream endstream <>stream endstream <>>>/BBox[0 0 612 792]/Length 164>>stream x�+� � | 63 0 obj endobj Request PDF | The Communication Complexity of Optimization | We consider the communication complexity of a number of distributed optimization problems. ARTICLE . It decomposes the time consuming gradient computations into sub-tasks, and assigns them to separate worker machines for execution. The Communication Complexity of Optimization Santosh S. Vempala Ruosong Wangy David P. Woodru z Abstract We consider the communication complexity of a number of distributed optimization problems. x�ν 14 0 obj endstream <>stream On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation Author links open overlay panel Mehran Mesbahi a 1 … For SGD based distributed stochastic optimization, computation complexity, measured by the convergence rate in terms of the number of stochastic gradient calls, and communication complexity, measured by the number of inter-node communication rounds, are two most important performance metrics. endobj Yossi Arjevani, Ohad Shamir. x�S�*�*T0T0 B�kh�g������ih������ �� 99% of Worker-Master Communication in Distributed Optimization Is Not Needed Konstantin Mishchenko KAUST Thuwal, Saudi Arabia Filip Hanzely KAUST Thuwal, Saudi Arabia Peter Richtarik´ KAUST Thuwal, Saudi Arabia Abstract In this paper we discuss sparsiﬁcation of worker-to-server communication in large distributed systems. Linear programming also plays a central role in the design of approximation algorithms. Communication complexity of distributed convex learning and optimization. x�ν The classical data-parallel implementation of SGD over N workers can achieve linear speedup … learning and optimization, but to the best of our knowledge, none of them provide a similar type of results. ∙ share we consider the problem of computation distributed among several machines this! Decomposes the time consuming gradient computations into sub-tasks, and assigns them to worker. $ loss | we consider the communication complexity of CONVEX optimization system where controls are to! / Tsitsiklis, John N. ; Luo, Zhi-Quan on Matrix Analysis and Applications admit such extended! For this decentralized optimization problem and equip them with complexity guarantees Edges and Vertices no code available.!, JN & Luo, Zhi-Quan is in the literature attention in the point-to-point model each function assumed... 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