
arXiv: 2208.13643
Decentralized optimization with orthogonality constraints is found widely in scientific computing and data science. Since the orthogonality constraints are nonconvex, it is quite challenging to design efficient algorithms. Existing approaches leverage the geometric tools from Riemannian optimization to solve this problem at the cost of high sample and communication complexities. To relieve this difficulty, based on two novel techniques that can waive the orthogonality constraints, we propose a variance-reduced stochastic gradient tracking (VRSGT) algorithm with the convergence rate of $O(1 / k)$ to a stationary point. To the best of our knowledge, VRSGT is the first algorithm for decentralized optimization with orthogonality constraints that reduces both sampling and communication complexities simultaneously. In the numerical experiments, VRSGT has a promising performance in a real-world autonomous driving application.
Large-scale problems in mathematical programming, FOS: Computer and information sciences, Computer Science - Machine Learning, Stiefel manifold, variance reduction, Stochastic programming, Machine Learning (stat.ML), Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Machine Learning (cs.LG), Nonlinear programming, Statistics - Machine Learning, Optimization and Control (math.OC), orthogonality constraints, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, decentralized optimization, stochastic gradient tracking, Mathematics - Optimization and Control
Large-scale problems in mathematical programming, FOS: Computer and information sciences, Computer Science - Machine Learning, Stiefel manifold, variance reduction, Stochastic programming, Machine Learning (stat.ML), Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Machine Learning (cs.LG), Nonlinear programming, Statistics - Machine Learning, Optimization and Control (math.OC), orthogonality constraints, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, decentralized optimization, stochastic gradient tracking, Mathematics - Optimization and Control
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