In this paper, we have in-depth and systematic research on the convergence rate of stochastic optimization problems; the least-square regression problem that the objective function consists of the L1 regular term is concerned and an effective accelerating stochastic approximation algorithm is proposed. Based on a non-strong convexity condition and using a smooth function to approximate the L1-regular term, the convergence speed of the learning algorithm is considered, and we obtain the convergence speed of the algorithm. This conclusion is superior to the previous convergence results.
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