Algorithm 1 Optimization

1:Input: $\mathbf{X},\mathbf{Y},\lambda$, m 2:Initialize: $\gamma =1$, $\eta =0.7$ (Samping rate) 3:Data Sampling: 4:for $k=1:m$   do 5:    Based on $\eta =0.7$, randomly generate subset index ${\Gamma }_k$ 6:    ${\mathbf{X}}^k={\mathbf{X}}_{{\Gamma }_k}$ 7:    ${\mathbf{Y}}^k={\mathbf{Y}}_{{\Gamma }_k}$ 8:end for 9:Proximal gradient descent: 10:repeat 11:    Compute gradient $\nabla L\left(\mathbf{W}\right(t\left)\right)$, set $\mathbf{A}=(\mathbf{W}\left(t\right)-{\displaystyle \frac{1}{\gamma }}\nabla L\left(\mathbf{W}\left(t\right)\right))$ 12:    for $j=1,2,\dots ,d$ do 13:         ${\mathbf{W}}_j={\left(1-{\displaystyle \frac{\lambda }{\parallel {\mathbf{A}}_j{\parallel }_2\gamma }}\right)}_{+}{\mathbf{A}}_j$ 14:    end for 15:    if $L\left({\mathbf{W}}^{\prime }\right)-L\left(\mathbf{W}\left(t\right)\right)<\dots$ then 16:         break and output $\mathbf{W}(t+1)={\mathbf{W}}^{\prime }$ 17:    else 18:         $\gamma =\gamma ·\alpha$ where $\alpha$ is user-defined 19:    end if 20:until convergence 21:Output: $\mathbf{W}(t+1)$