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This paper studies non-smooth problems of convex stochastic optimization.Using the smoothing technique based on the replacement of the function value atthe considered point by the averaged function value over a ball (in $l_1$-normor $l_2$-norm) of small radius with the center in this point, the originalproblem is reduced to a smooth problem (whose Lipschitz constant of thegradient is inversely proportional to the radius of the ball). An importantproperty of the smoothing used is the possibility to calculate an unbiasedestimation of the gradient of a smoothed function based only on realizations ofthe original function. The obtained smooth stochastic optimization problem isproposed to be solved in a distributed federated learning architecture (theproblem is solved in parallel: nodes make local steps, e.g. stochastic gradientdescent, then they communicate - all with all, then all this is repeated). Thegoal of this paper is to build on the current advances in gradient-freenon-smooth optimization and in feild of federated learning, gradient-freemethods for solving non-smooth stochastic optimization problems in federatedlearning architecture.

Gradient-Free Federated Learning Methods with $l_1$ and $l_2$-Randomization for Non-Smooth Convex Stochastic Optimization Problems