An Accelerated Method for Derivative-Free Smooth Stochastic Convex Optimization

We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations its values, the noise consisting two parts. Similar to stochastic optimization problems, first part nature. The second additive unknown nature but bounded in absolute value. In two-point feedback setting, i.e., when pairs values are available, we propose accelerated derivative-free algorithm together with complexity analysis. bound our by factor $\sqrt{n}$ larger than for gradient-based algorithms, where $n$ dimension decision variable. also nonaccelerated similar gradient--based algorithm; that is, does not have any dimension-dependent except logarithmic. Notably, if difference between starting point and solution sparse vector, both obtain better uses 1-norm proximal setup rather Euclidean setup, standard choice problems.