Online estimation of the inverse of the Hessian for stochastic optimization with application to universal stochastic Newton algorithms

Abstract

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.

References in corpus (4)

• Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm
• Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity
• An efficient Averaged Stochastic Gauss-Newton algorithm for estimating parameters of non linear regressions models
• Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Streaming Data