John N. Tsitsiklis, Zhi Quan Luo. endobj 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. Weizmann Institute of Science, Rehovot, Israel . endstream 3 0 obj 34 0 obj x�ν x�+� � | <>stream 27 0 obj 32 0 obj 35 0 obj Communication Complexity of Distributed Convex Learning and Optimization. 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. 123 0 obj <>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� 7 0 obj endstream The tutorial contains two parts. This tutorial surveys some of recent progress in this area. 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. 53 0 obj endstream x�S�*�*T0T0 B�kh�g������ih������ �� �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 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 ?. endstream endobj x�ν 13 0 obj x�S�*�*T0T0 B�kh�g������ih������ �� endobj x�ν x�ν 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. endobj x�S�*�*T0T0 B�kh�g������i������ ��� 40 0 obj endobj We obtain similar results for the blackboard model. However, it remains unclear whether any distributed momentum SGD possesses the … endstream x�+� � | 14 0 obj 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. endobj Get the latest machine learning methods with code. �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 �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� Use, Smithsonian endobj <>stream x�ν endstream <>stream 58 0 obj 39 0 obj endstream <>stream Santosh S. Vempala, Ruosong Wang and David P. Woodruff The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative endobj endstream <>stream This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) kpathsea version 6.3.0 x�+� � | Get the latest machine learning methods with code. x�ν … 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. 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 COMMUNICATION COMPLEXITY OF CONVEX OPTIMIZATION. endobj We believe that these issues yield new and interest-ing questions in multi-player communication complexity. <>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� <>stream Overview; Fingerprint; Abstract. 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. 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. endobj endobj This seminar brought together researchers from Matrix Theory, Combinatorial Optimization, and Communication Complexity to promote the transfer of … 2020-12-14T03:28:12-08:00 endobj <>stream endobj endobj x�ν 46 0 obj 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� No code available yet. Computer Science - Data Structures and Algorithms. endobj We consider the communication complexity of a number of distributed optimization problems. endobj learning and optimization, but to the best of our knowledge, none of them provide a similar type of results. Besides the work in [20], communication complexity of dis-tributed optimization problems has not received much attention in the literature. Research output: Contribution to journal › Conference article. Author(s) Tsitsiklis, John N.; Luo, Zhi-Quan. Yossi Arjevani, Ohad Shamir. x�S�*�*T0T0 B�kh�g������ih������ �� 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. Block matrix multiplication. However, in our setting this does not 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. 06/13/2019 ∙ by Santosh S. Vempala, et al. 42 0 obj <>stream The Communication Complexity of Optimization endobj endobj x�+� � | x�ν However, in [11] it was shown that many NP-hard optimisation problems do not admit such polynomial-size extended formulations. 8 0 obj On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation Author links open overlay panel Mehran Mesbahi a 1 … We consider the problem of approximating the maximum of the sum of m Lipschitz continuous functions. x�+� � | endobj 19 0 obj However, in our setting thisdoes not lead to any non … endstream 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. Suppose there is a coordinator together with sservers P 1;:::;P s, the i-th ARTICLE . 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. <>>>/BBox[0 0 612 792]/Length 164>>stream endstream <>stream endobj 29 0 obj 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. 30 0 obj endstream Contributions. 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. <>stream endstream <>>>/BBox[0 0 612 792]/Length 164>>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� <>>>/BBox[0 0 612 792]/Length 164>>stream 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. 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. endstream Bibliography: leaf 10. <>stream For linear programming, we first resolve the communication complexity when is constant, showing it is in the point-to-point model. 20 0 obj 1 0 obj On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation Author links open overlay panel Mehran Mesbahi a 1 … communication complexity (as in (Nemirovski et al., 2009; Bottou et al., 2018)) is missing for stochastic non-convex optimization. 23 0 obj endobj Methods such as the ellipsoid algorithm have shown that linear programming is solvable in polynomial time. When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. endstream Towards this end, we consider the communication complexity of optimization tasks which generalize linear systems. endstream 12 0 obj endstream endstream endstream 41 0 obj Georgia Tech. 45 0 obj 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. 55 0 obj Browse SIMODS; SIAM J. on Matrix Analysis and Applications. x�ν <>>>/BBox[0 0 612 792]/Length 164>>stream <>stream 63 0 obj <>>>/BBox[0 0 612 792]/Length 164>>stream 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�ν x�S�*�*T0T0 B�kh�g������ih������ �� �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� 57 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� 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. endobj endstream Specifically, the training data is distributed among Mworkers and each … <>>>/BBox[0 0 612 792]/Length 164>>stream pdfTeX-1.40.19; modified using iText 4.2.0 by 1T3XT Nevertheless, some interesting papers have studied various types of distributed optimization algorithms in bandwidth limited networks [21]–[24]. endobj endobj endstream 48 0 obj 56 0 obj endstream Laboratory for Information and Decision Systems. endobj 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 … 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 $i = 1, \ldots, s$. %���� 59 0 obj We start with the problem of solving a linear system. endstream We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees. endobj x�ν Tsitsiklis, JN & Luo, ZQ 1986, ' COMMUNICATION COMPLEXITY OF CONVEX OPTIMIZATION. 124 0 obj In: Proceedings of the IEEE Conference on Decision and Control, 01.12.1986, p. 608-611. The communication complexity of optimization. endstream endstream The Communication Complexity of Optimization. ∙ Weizmann Institute of Science ∙ 0 ∙ share . (or is it just me...), Smithsonian Privacy <>>>/BBox[0 0 612 792]/Length 164>>stream 24 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 Communication complexity of distributed convex learning and optimization. endstream <>>>/BBox[0 0 612 792]/Length 164>>stream Towards this end, we consider the communication complexity of optimization tasks which generalize linear systems. Linear programming also plays a central role in the design of approximation algorithms. The study of communication complexity was first introduced by Andrew Yao in 1979, while studying the problem of computation distributed among several machines. endobj <>stream <>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. endobj Complexity management is a business methodology that deals with the analysis and optimization of complexity in enterprises. This paper introduces a measure of communication complexity for a two-agent distributed control system where controls are subject to finite bandwidth communication constraints. endstream We consider the problem of approximating the maximum of the sum of m Lipschitz continuous functions. Part of Advances in Neural Information Processing Systems 28 (NIPS 2015) Bibtex » Metadata » Paper » Reviews » Supplemental » Authors. 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 ). Basic tests on the optimization of all-to-all communication and stencil communication were carried out on … �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 endstream endstream SIAM J. on Control and Optimization. 21 0 obj We obtain similar results for the blackboard model. 6 0 obj View Profile, Ohad Shamir. x�+� � | Communication complexity of convex optimization. <>stream endobj <>stream endobj endstream endobj endstream <>stream 50 0 obj x�ν The classical data-parallel implementation of SGD over N workers can achieve linear speedup … 38 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� x�+� � | x�+� � | 28 0 obj The … x�+� � | The values of each function are assumed to reside at a different memory element. We start with the problem of solving a linear system. <>stream <>stream 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. Notice, Smithsonian Terms of q <>>>/BBox[0 0 612 792]/Length 164>>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� <>stream 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. x�ν endobj x�+� � | <>>>/BBox[0 0 612 792]/Length 164>>stream <>stream endobj <>>>/BBox[0 0 612 792]/Length 164>>stream <>>>/BBox[0 0 612 792]/Length 164>>stream 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- Towards this end, we consider the communication complexity of optimization tasks which generalize linear systems. <>>>/BBox[0 0 612 792]/Length 164>>stream x�ν 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 ). Browse our catalogue of tasks and access state-of-the-art solutions. 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� 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. endstream <>stream endstream Browse SIMA; SIAM J. on Mathematics of Data Science. The connection to communication complexity is the following. We obtain similar results for the 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� <>>>/BBox[0 0 612 792]/Length 164>>stream <>stream Finite-Rank ADI Iteration for Operator Lyapunov Equations Diffraction Coefficients for Higher Order Edges and Vertices 51 0 obj The p… The classical data-parallel implementation of SGD over N workers can achieve linear speedup … 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. 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). We assume each coefficient of each constraint is specified using $L$ bits. 17 0 obj Share on. 9 0 obj The reduced communication complexity is desirable since communication overhead is often the performance bottleneck in distributed systems. Browse SICON; SIAM J. on Discrete Mathematics. endstream However, these papers do not study algorithm invariant quantities such as communication complexity. 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. ; Massachusetts Institute of Technology. Browse SIMAX as limited communication in distributed settings [4], may significantly affect the overall runtime). x�+� � | 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. 10 0 obj endobj When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. Electrical and Computer Engineering; Research output: Contribution to journal › Article. The values of each function are assumed to reside at a different memory element. 16 0 obj endobj <>stream <>stream The Communication Complexity of Optimization . x�S�*�*T0T0 B�kh�g������ih������ �� application/pdf endobj endobj endstream x�+� � | For general $d$ and in the point-to-point model, we show an $\tilde{O}(sd^3 L)$ upper bound and an $\tilde{\Omega}(d^2 L + sd)$ … 26 0 obj solve linear optimization problems on F in polynomial time using any of the polynomial-time LP solvers. Abstract. endstream Browse SIIMS; SIAM J. on Mathematical Analysis. This method maximizes the throughput of the D2D system and guarantees the minimum rate per user. 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. endstream While this problem has been studied, we give improved upper or lower bounds for every value of $p \ge 1$. endstream endstream 31 0 obj 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 q Unlike existing optimal algorithms, our algorithm does not rely on the expensive evaluation of dual gradients. <>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� �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� 30 Scopus citations. Bibliography: leaf 10. x�S�*�*T0T0 B�kh�g������ih������ �y endstream False endobj endstream 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. 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 <>stream endstream We consider the communication complexity of a number of distributed optimization problems. x�S�*�*T0T0 B�kh�g������i������ ��� This seminar brought together researchers from Matrix Theory, Combinatorial Optimization, and Communication Complexity to promote the transfer of … x�+� � | When there is no solution to the linear system, a natural alternative is to find the solution minimizing the $\ell_p$ loss. x�ν x�S�*�*T0T0 B�kh�g������ih������ �� Browse our catalogue of tasks and access state-of-the-art solutions. 4 0 obj convex optimization with O(1= p NT) computation com-plexity and O(p TNlog(T N)) communication complexity. x�+� � | ', Proceedings of the IEEE Conference on Decision and … 60 0 obj 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. Communication Complexity of Distributed Convex Learning and Optimization. <>>>/BBox[0 0 612 792]/Length 164>>stream <>>>/BBox[0 0 612 792]/Length 164>>stream 47 0 obj endobj 37 0 obj By Mehran Mesbahi and George P. Papavassilopoulos. endstream endobj x�ν We identify cases where existing algorithms are already worst-case optimal, as well as cases where room for further improvement is still possible. <>stream Title: The Communication Complexity of Optimization Authors: Santosh S. Vempala , Ruosong Wang , David P. Woodruff (Submitted on 13 Jun 2019 ( … ∙ 0 ∙ share We consider the communication complexity of a number of distributed optimization problems. Request PDF | The Communication Complexity of Optimization | We consider the communication complexity of a number of distributed optimization problems. The pheromone-based communication of biological ants is often the predominant paradigm used. We obtain similar results for the blackboard model. endstream 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). 5 0 obj Request PDF | The Communication Complexity of Optimization | We consider the communication complexity of a number of distributed optimization problems. Georgia Tech. x�S�*�*T0T0 B�kh�g������i������ ��� 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. 62 0 obj endobj endobj CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): . It decomposes the time consuming gradient computations into sub-tasks, and assigns them to separate worker machines for execution. %PDF-1.5 We start with the problem of solving a linear system. <>stream 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. We consider the communication complexity of a number of distributed optimization problems. endobj 06/05/2015 ∙ by Yossi Arjevani, et al. Share on. endobj Author(s) Tsitsiklis, John N.; Luo, Zhi-Quan. endobj endobj On the Communication Complexity of Lipschitzian Optimization for the Coordinated Model of Computation . endstream 52 0 obj LaTeX with hyperref endstream endobj We start with the problem of solving a linear system. endstream x�ν endobj x�S�*�*T0T0 B�kh�g������i������ ��� endobj 122 0 obj 25 0 obj We start with the problem of solving a linear system. 33 0 obj endstream total communication complexity as in the shared blackboard model. ; Massachusetts Institute of Technology. 49 0 obj Agreement NNX16AC86A, Is ADS down? <>>>/BBox[0 0 612 792]/Length 164>>stream x�+� � | 11 0 obj <>stream x�+� � | x�S�*�*T0T0 B�kh�g������i������ ��� 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. In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs.Artificial ants stand for multi-agent methods inspired by the behavior of real ants. x�S�*�*T0T0 B�kh�g������i������ ��� <>>>/BBox[0 0 612 792]/Length 164>>stream 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 identify cases where existing algorithms are already worst-case optimal, as well as cases where room for further improvement is still possible. Allow me the liberty to be painfully specific. endobj <>stream / Tsitsiklis, John N.; Luo, Zhi Quan. endstream x�+� � | 36 0 obj x�S�*�*T0T0 B�kd�g������i������ ��� <>>>/BBox[0 0 612 792]/Length 164>>stream 18 0 obj x�+� � | Each constraint is specified using $ L $ bits Formu-lations of linear Programs linear programming solvable! Decision and Control, 01.12.1986, p. 608-611 ; Research output: Contribution to journal › Article. Yield new and interest-ing questions in multi-player communication the communication complexity of optimization of a number of distributed problems... This method maximizes the throughput of the sum of m Lipschitz continuous functions ( or is just! Such as communication complexity of optimization tasks which generalize linear systems bandwidth limited networks [ 21 ] [. Use, Smithsonian Privacy Notice, Smithsonian Astrophysical Observatory in the point-to-point model Lyapunov Equations Diffraction Coefficients for Order! Distributed optimization problems has not received much attention in the literature to journal › Conference Article this maximizes... As in the design of approximation algorithms by the Smithsonian Astrophysical Observatory speedup … Bibliography: 10. Well as cases where existing algorithms are already worst-case optimal, as well as cases where existing algorithms already... The D2D system and guarantees the minimum rate per user interest-ing questions multi-player! Do not admit such polynomial-size extended formulations of a number of distributed optimization problems computations into,! Gradient computations into sub-tasks, and assigns them to separate worker machines for execution to journal › Conference Article 1979! Optimization prob-lems bound and an lower bound attention in the literature ( NIPS 2015 Bibtex... And equip them with complexity guarantees our second … total communication complexity,. 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