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Using double-smoothing technique and stochastic mirror descent with inexactoracle we built an optimal algorithm (up to a multiplicative factor) fortwo-points gradient-free non-smooth stochastic convex programming. Weinvestigate how much can be the level of noise (the nature of this noise isn'tnecessary stochastic) for the rate of convergence to be maintained (up to amultiplicative factor).

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