Stochastic quasi-Newton with line-search regularisation

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally attractive algorithms. In essence, this is achieved by learning the second-order (Hessian) information based on observing first-order gradients. We extend these ideas to the stochastic setting by employing a highly flexible model for the Hessian and infer its value based on observing noisy gradients. In addition, we propose a stochastic counterpart to standard line-search procedures and demonstrate the utility of this combination on maximum likelihood identification for general nonlinear state space models. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper introduces a novel quasi-Newton algorithm for stochastic optimization, extending the rapid convergence and computational attractiveness seen in deterministic optimization problems. The algorithm learns second-order information based on observing first-order gradients, with a highly flexible model for the Hessian. A stochastic counterpart to standard line-search procedures is proposed and demonstrated to be useful in maximum likelihood identification for general nonlinear state space models.