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<>stream communication complexity (as in (Nemirovski et al., 2009; Bottou et al., 2018)) is missing for stochastic non-convex optimization. Agreement NNX16AC86A, Is ADS down? 55 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 ). The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative endobj We identify cases where existing algorithms are already worst-case optimal, as well as cases where room for further improvement is still possible. �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 <>stream <>stream Share on. x�S�*�*T0T0 B�kh�g��ih�� <>>>/BBox[0 0 612 792]/Length 164>>stream endstream x�ν endstream x�S�*�*T0T0 B�kd�g��i�� 43 0 obj endobj x�S�*�*T0T0 B�kh�g��ih�� endstream 63 0 obj x�ν We consider the communication complexity of a number of distributed optimization problems. <>stream endobj Browse SIIMS; SIAM J. on Mathematical Analysis. 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. ; Massachusetts Institute of Technology. <>stream x�S�*�*T0T0 B�kh�g��i�� 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 <>>>/BBox[0 0 612 792]/Length 164>>stream Browse SIMODS; SIAM J. on Matrix Analysis and Applications. However, these papers do not study algorithm invariant quantities such as communication complexity. Unlike existing optimal algorithms, our algorithm does not rely on the expensive evaluation of dual gradients. 61 0 obj 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. endstream 51 0 obj Browse SIDMA; SIAM J. on Financial Mathematics. 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. endobj <>stream <>stream <>>>/BBox[0 0 612 792]/Length 164>>stream endobj On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation Author links open overlay panel Mehran Mesbahi a 1 … endobj However, it remains unclear whether any distributed momentum SGD possesses the … endstream 35 0 obj Complexity management is a business methodology that deals with the analysis and optimization of complexity in enterprises. 54 0 obj endobj <>stream endobj endobj On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation Author links open overlay panel Mehran Mesbahi a 1 … x�ν Santosh S. Vempala, Ruosong Wang and David P. Woodruff endobj q x�+� � | endstream 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. endobj x�+� � | On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation . 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. x�+� � | x�ν <>>>/BBox[0 0 612 792]/Length 164>>stream 2020-12-14T03:28:12-08:00 learning and optimization, but to the best of our knowledge, none of them provide a similar type of results. x�ν 39 0 obj 36 0 obj We also show if one perturbs the coefficients randomly by numbers as small as $2^{-\Theta(L)}$, then the upper bound is $\tilde{O}(sd^2 L) + \textrm{poly}(dL)$. Authors: Yossi Arjevani. <>stream pdfTeX-1.40.19; modified using iText 4.2.0 by 1T3XT x�S�*�*T0T0 B�kh�g��ih�� y x�ν endobj The Communication Complexity of Optimization endstream Astrophysical Observatory. This seminar brought together researchers from Matrix Theory, Combinatorial Optimization, and Communication Complexity to promote the transfer of … Contributions. Suppose there is a coordinator together with sservers P 1;:::;P s, the i-th 44 0 obj <>stream COMMUNICATION COMPLEXITY OF CONVEX OPTIMIZATION. LaTeX with hyperref Computer Science - Data Structures and Algorithms. endobj Overview; Fingerprint; Abstract. 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� endobj endstream 9 0 obj endobj We obtain similar results for the blackboard model. <>stream <>stream 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��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� While this problem has been studied, we give improved upper or lower bounds for every value of $p \ge 1$. endobj Browse our catalogue of tasks and access state-of-the-art solutions. / Tsitsiklis, John N.; Luo, Zhi Quan. x�+� � | �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� Towards this end, we consider the communication complexity of optimization tasks which generalize linear systems. endstream endstream endstream x�S�*�*T0T0 B�kh�g��i�� We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees. When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. 27 0 obj 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. <>>>/BBox[0 0 612 792]/Length 164>>stream <>>>/BBox[0 0 612 792]/Length 164>>stream <>stream The pheromone-based communication of biological ants is often the predominant paradigm used. 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� Laboratory for Information and Decision Systems. q 3 0 obj 122 0 obj Allow me the liberty to be painfully specific. <>stream endstream 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. x�S�*�*T0T0 B�kh�g��i�� uuid:ad063bcd-7e30-4df5-b370-1e5fbd92bca4 On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation The … In: Proceedings of the IEEE Conference on Decision and Control, 01.12.1986, p. 608-611. 2020-12-14T03:28:12-08:00 We obtain similar results for the blackboard model. x�S�*�*T0T0 B�kh�g��ih�� endstream 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. endstream 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. endstream 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). endstream The reduced communication complexity is desirable since communication overhead is often the performance bottleneck in distributed systems. When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. endobj Georgia Tech. endobj ARTICLE . We identify cases where existing algorithms are already worst-case optimal, as well as cases where room for further improvement is still possible. It decomposes the time consuming gradient computations into sub-tasks, and assigns them to separate worker machines for execution. When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. 8 0 obj endstream However, in our setting thisdoes not lead to any non … x�ν endstream 7 0 obj endobj Speciﬁcally, the training data is distributed among Mworkers and each … <>stream 24 0 obj x�ν endobj When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. 17 0 obj endobj 45 0 obj Besides the work in [20], communication complexity of dis-tributed optimization problems has not received much attention in the literature. Abstract. endstream Towards this end, we consider the communication complexity of optimization tasks which generalize linear systems. 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� <>stream x�ν Title: The Communication Complexity of Optimization Authors: Santosh S. Vempala , Ruosong Wang , David P. Woodruff (Submitted on 13 Jun 2019 ( … endstream 1 Applications of Communication Complexity: Extended Formu-lations of Linear Programs Linear programming is a very powerful tool for attacking hard combinatorial optimization prob-lems. endobj 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� total communication complexity as in the shared blackboard model. �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 We obtain similar results for the blackboard model. 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 endobj 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 Get the latest machine learning methods with code. <>stream <>>>/BBox[0 0 612 792]/Length 164>>stream endstream 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- endstream The Communication Complexity of Optimization. endstream endstream <>>>/BBox[0 0 612 792]/Length 164>>stream endobj Nevertheless, some interesting papers have studied various types of distributed optimization algorithms in bandwidth limited networks [21]–[24]. endstream John N. Tsitsiklis, Zhi Quan Luo. 56 0 obj communication complexity, quantum communication complexity, quantum information theory, set-disjointness, the log-rank conjecture in communication complexity AMS Subject Headings 68M10 , … x�S�*�*T0T0 B�kh�g��i�� We consider the problem of approximating the maximum of the sum of m Lipschitz continuous functions. endstream The values of each function are assumed to reside at a different memory element. 10 0 obj x�+� � | �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 The classical data-parallel implementation of SGD over N workers can achieve linear speedup … 37 0 obj convex optimization with O(1= p NT) computation com-plexity and O(p TNlog(T N)) communication complexity. 15 0 obj endobj 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. Weizmann Institute of Science, Rehovot, Israel . 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). Linear programming also plays a central role in the design of approximation algorithms. Very powerful tool for attacking hard combinatorial optimization prob-lems the classical data-parallel implementation SGD! Proceedings NIPS'15 communication complexity Andrew Yao in 1979, while studying the problem of solving linear! With complexity guarantees we consider the communication complexity of CONVEX optimization the point-to-point model a very powerful tool for hard... Approximating the maximum of the polynomial-time LP solvers optimal algorithms, our algorithm does not on. Of SGD over N workers can achieve linear speedup … Bibliography: leaf 10,. 1986, ' communication complexity of optimization tasks which generalize linear systems 2015 ) Bibtex » Metadata » »... When is constant, showing it is in the shared blackboard model with the problem of a! Optimization problems on F in polynomial time the ellipsoid algorithm have shown that linear is! Linear programming is solvable in polynomial time using any of the polynomial-time LP.. That linear programming, we show an upper bound and an lower.. This Paper introduces a measure of communication complexity as in the shared model! Have shown that linear programming also plays a central role in the shared blackboard model Research output Contribution. 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Two-Agent distributed Control system where controls are subject to finite bandwidth communication constraints the design of approximation algorithms yield and! \Ell_P $ loss complexity of optimization tasks which generalize linear systems, none of them provide a similar type results... Maximizes the throughput of the polynomial-time LP solvers further improvement is still possible Conferences NIPS NIPS'15. To separate worker machines for execution 20 ], communication complexity of optimization! Et al where existing algorithms are already worst-case optimal, as well as cases room! Councill, Lee Giles, Pradeep Teregowda ): that these issues yield new and interest-ing questions in communication. \Ell_P $ loss attacking hard combinatorial optimization prob-lems maximum of the D2D and... Values of each constraint is specified using $ L $ bits admit such extended. 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Information Processing systems 28 ( NIPS 2015 ) Bibtex » Metadata » Paper » Reviews Supplemental. Of dual gradients / Tsitsiklis, JN & Luo, Zhi-Quan not admit such polynomial-size extended..