Gradient-Free Methods for Stochastic Convex Optimization with Stochastic Functional Constraints

We study convex stochastic optimization with $m$ expectation constraints, $\min\{f(x)=\E F(x,ξ):\ g_i(x)=\E G_i(x,ξ)\le 0,\ i=1,\dots,m,\ x\in \Q\}$, when only noisy function values are available. At each call the oracle returns the vector $(F(x,ξ),G_1(x,ξ),\dots,G_m(x,ξ))$ at two points, with the s