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Research on three-step accelerated gradient algorithm in deep learning

Statistical Theory and Related Fields 2022年第1期6卷 40-57页

作者： Yongqiang Lian Yincai Tang Shirong Zhou KLATASDS-MOE School of StatisticsEast China Normal UniversityShanghaiPeople's Republic of China

Gradient descent(GD)algorithm is the widely used optimisation method in training machine learning and deep learning *** this paper,based on GD,Polyak’s momentum(PM),and Nesterov accelerated gradient(NAG),we give the convergence of the algorithms from an ini-tial value to the optimal value of an objective function in simple quadratic *** on the convergence property of the quadratic function,two sister sequences of NAG’s iteration and par-allel tangent methods in neural networks,the three-step accelerated gradient(TAG)algorithm is proposed,which has three sequences other than two sister *** illustrate the perfor-mance of this algorithm,we compare the proposed algorithm with the three other algorithms in quadratic function,high-dimensional quadratic functions,and nonquadratic *** we consider to combine the TAG algorithm to the backpropagation algorithm and the stochastic gradient descent algorithm in deep *** conveniently facilitate the proposed algorithms,we rewite the R package‘neuralnet’and extend it to‘supneuralnet’.All kinds of deep learning algorithms in this paper are included in‘supneuralnet’***,we show our algorithms are superior to other algorithms in four case studies.

关键词： accelerated algorithm backpropagation deep learning learning rate momentum stochastic gradient descent

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A Data-driven Variable Reduction Approach for Transmission-constrained Unit Commitment of Large-scale Systems

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Journal of Modern Power Systems and Clean Energy 2023年第1期11卷 254-266页

作者： Yuzhou Zhou Qiaozhu Zhai Lei Wu Moammad Shahidehpour Systems Engineering Institute MOEKLINNS LabXi’an Jiaotong UniversityXi’an 710049China Electrical and Computer Engineering Department Stevens Institute of TechnologyHobokenU.S. Electrical and Computer Engineering Department Illinois Institute of TechnologyChicagoU.S. IEEE

This paper presents a data-driven variable reduction approach to accelerate the computation of large-scale transmission-constrained unit commitment(TCUC).Lagrangian relaxation(LR)and mixed-integer linear programming(MILP)are popular approaches to solving ***,with many binary unit commitment variables,LR suffers from slow convergence and MILP presents heavy computation *** proposed data-driven variable reduction approach consists of offline and online calculations to accelerate computational performance of the MILP-based large-scale TCUC problems.A database including multiple nodal net load intervals and the corresponding TCUC solutions is first built offline via the data-driven and all-scenario-feasible(ASF)approaches,which is then leveraged to efficiently solve new TCUC instances ***/off statuses of considerable units can be fixed in the online calculation according to the database,which would reduce the computation burden while guaranteeing good solution quality for new TCUC instances.A feasibility proposition is proposed to promptly check the feasibility of the new TCUC instances with fixed binary variables,which can be used to dynamically tune parameters of binary variable fixing strategies and guarantee the existence of feasible UC solutions even when system structure *** tests illustrate the efficiency of the proposed approach.

关键词： Unit commitment accelerated algorithm data driven variable reduction

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