  This letter presents an almost sure convergence of the zeroth-order mirror
descent algorithm. The algorithm admits non-smooth convex functions and a
biased oracle which only provides noisy function value at any desired point. We
approximate the subgradient of the objective function using Nesterov's Gaussian
Approximation (NGA) with certain alternations suggested by some practical
applications. We prove an almost sure convergence of the iterates' function
value to the neighbourhood of optimal function value, which can not be made
arbitrarily small, a manifestation of a biased oracle. This letter ends with a
concentration inequality, which is a finite time analysis that predicts the
likelihood that the function value of the iterates is in the neighbourhood of
the optimal value at any finite iteration.
