  Distributed optimization has a rich history. It has demonstrated its
effectiveness in many machine learning applications, etc. In this paper we
study a subclass of distributed optimization, namely decentralized optimization
in a non-smooth setting. Decentralized means that $m$ agents (machines) working
in parallel on one problem communicate only with the neighbors agents
(machines), i.e. there is no (central) server through which agents communicate.
And by non-smooth setting we mean that each agent has a convex stochastic
non-smooth function, that is, agents can hold and communicate information only
about the value of the objective function, which corresponds to a gradient-free
oracle. In this paper, to minimize the global objective function, which
consists of the sum of the functions of each agent, we create a gradient-free
algorithm by applying a smoothing scheme via $l_2$ randomization. We also
verify in experiments the obtained theoretical convergence results of the
gradient-free algorithm proposed in this paper.
