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. 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). x�S�*�*T0T0 B�kh�g������ih������ �� x�+� � | 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. 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. 10 0 obj 45 0 obj Communication Complexity of Distributed Convex Learning and Optimization. Laboratory for Information and Decision Systems. endstream x�ν 24 0 obj x�ν 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� endstream endstream x�+� � | ; Massachusetts Institute of Technology. uuid:ad063bcd-7e30-4df5-b370-1e5fbd92bca4 total communication complexity as in the shared blackboard model. endobj endstream 16 0 obj endstream 1 0 obj 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� �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�ν <>stream This seminar brought together researchers from Matrix Theory, Combinatorial Optimization, and Communication Complexity to promote the transfer of … endstream Author(s) Tsitsiklis, John N.; Luo, Zhi-Quan. 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. Santosh S. Vempala, Ruosong Wang and David P. Woodruff 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). We also show if one perturbs the coefficients randomly by numbers as small as $2^{-\Theta(L)}$, then the upper bound is $\tilde{O}(sd^2 L) + \textrm{poly}(dL)$. <>>>/BBox[0 0 612 792]/Length 164>>stream However, these papers do not study algorithm invariant quantities such as communication complexity. endobj 37 0 obj However, in [11] it was shown that many NP-hard optimisation problems do not admit such polynomial-size extended formulations. x�ν endstream Browse SIIMS; SIAM J. on Mathematical Analysis. solve linear optimization problems on F in polynomial time using any of the polynomial-time LP solvers. endobj 122 0 obj <>>>/BBox[0 0 612 792]/Length 164>>stream endobj 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. Astrophysical Observatory. ; Massachusetts Institute of Technology. x�+� � | Research output: Contribution to journal › Conference article. �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�S�*�*T0T0 B�kh�g������ih������ �y 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. 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. The connection to communication complexity is the following. <>stream <>>>/BBox[0 0 612 792]/Length 164>>stream endobj 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. We start with the problem of solving a linear system. endobj We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees. 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 ). 36 0 obj Abstract. 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