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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2021, Vol. 34 
