A Stochastic Quasi-Newton Method for Large-Scale Optimization
This addresses the problem of noisy curvature estimates in large-scale optimization for machine learning practitioners, but appears incremental as it adapts classical techniques to a stochastic setting.
The paper tackles the challenge of incorporating curvature information in stochastic optimization by proposing a stochastic quasi-Newton method that uses limited-memory BFGS with pointwise Hessian-vector products, showing promising results on machine learning problems.
The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper, we propose a stochastic quasi-Newton method that is efficient, robust and scalable. It employs the classical BFGS update formula in its limited memory form, and is based on the observation that it is beneficial to collect curvature information pointwise, and at regular intervals, through (sub-sampled) Hessian-vector products. This technique differs from the classical approach that would compute differences of gradients, and where controlling the quality of the curvature estimates can be difficult. We present numerical results on problems arising in machine learning that suggest that the proposed method shows much promise.