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| Individual Convergence of Projected Dual Averaging Methods in Nonsmooth Convex Cases |
| QU Junyi1, BAO Lei1 , TAO Qing1 |
| 1. Department of Information Engineering, Chinese Academy of People′s Liberation Army Artillery Air Defense Academy,Hefei 230031 |
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Abstract For convex problems, since the convergence analysis of DA(dual averaging) needs to be transformed in dual space, it is difficult to gain individual convergence. In this paper, a simple convergence analysis of DA is presented, and then it is proved that DA can attain the same optimal Ο(lnt/t) individual convergence rate as gradient descent(GD). Different from GD, the individual convergence of DA is proved to be step-size flexible by analyzing two typical step-size strategies. Furthermore, the stochastic version of the derived convergence is extended to solve large-scale machine learning problems. Experiments on L1-norm constrained hinge loss problems verify the correctness of the theoretical analysis.
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Received: 17 August 2020
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| Fund:National Natural Science Foundation of China(No.61673394,620706252), Natural Science Foundation of Anhui Province(No.1908085MF193) |
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Corresponding Authors:
TAO Qing, Ph.D. professor. His research interests include pa-ttern recognition, machine learning and applied mathematics.
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About author:: QU Junyi, master student. His research interests include convex optimization algorithm and its application in machine lear-ning.
BAO Lei, Ph.D. candidate. Her research interests include convex optimization algorithm and its application in machine learning. |
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2021, Vol. 34 
