  This paper addresses second-order stochastic optimization for estimating the
minimizer of a convex function written as an expectation. A direct recursive
estimation technique for the inverse Hessian matrix using a Robbins-Monro
procedure is introduced. This approach enables to drastically reduces
computational complexity. Above all, it allows to develop universal stochastic
Newton methods and investigate the asymptotic efficiency of the proposed
approach. This work so expands the application scope of secondorder algorithms
in stochastic optimization.
