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Stochastic optimization lies at the core of most statistical learning models.The recent great development of stochastic algorithmic tools focusedsignificantly onto proximal gradient iterations, in order to find an efficientapproach for nonsmooth (composite) population risk functions. The complexity offinding optimal predictors by minimizing regularized risk is largely understoodfor simple regularizations such as $\ell_1/\ell_2$ norms. However, more complexproperties desired for the predictor necessitates highly difficult regularizersas used in grouped lasso or graph trend filtering. In this chapter we developand analyze minibatch variants of stochastic proximal gradient algorithm forgeneral composite objective functions with stochastic nonsmooth components. Weprovide iteration complexity for constant and variable stepsize policiesobtaining that, for minibatch size $N$, after$\mathcal{O}(\frac{1}{N\epsilon})$ iterations $\epsilon-$suboptimality isattained in expected quadratic distance to optimal solution. The numericaltests on $\ell_2-$regularized SVMs and parametric sparse representationproblems confirm the theoretical behaviour and surpasses minibatch SGDperformance.

Stochastic Proximal Gradient Algorithm with Minibatches. Application to Large Scale Learning Models