Gradient-free two-points optimal method for non smooth stochastic convex optimization problem with additional small noise

Understand

Using double-smoothing technique and stochastic mirror descent with inexact oracle we built an optimal algorithm (up to a multiplicative factor) for two-points gradient-free non-smooth stochastic convex programming.

• We investigate how much can be the level of noise (the nature of this noise isn't necessary stochastic) for the rate of convergence to be maintained (up to a multiplicative factor).