Stochastic quasi-Newton with line-search regularization
This work addresses the challenge of efficient optimization in stochastic settings, which is incremental as it adapts existing deterministic methods to noisy gradients.
The paper tackled the problem of extending quasi-Newton methods to stochastic optimization by proposing a novel algorithm with a flexible Hessian model and a stochastic line-search procedure, demonstrating its utility on maximum likelihood identification for nonlinear state space models.
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.