  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.
