Optimal Convergence Rate of the Randomized Algorithms of Stochastic Approximation in Arbitrary Noise

Multidimensional stochastic optimization plays an important role in analysis and control of many technical systems. To solve the challenging multidimensional problems of optimization, it was suggested to use the randomized algorithms of stochastic approximation with perturbed input which are not just simple, but also provide consistent estimates of the unknown parameters for observations in “almost arbitrary” noise. Optimal methods of choosing the parameters of algorithms were motivated.