A Linearly-Convergent Stochastic L-BFGS Algorithm
This work addresses optimization challenges in machine learning and data science, offering an incremental improvement by combining existing stochastic L-BFGS and variance reduction techniques.
The authors tackled the problem of large-scale optimization by proposing a new stochastic L-BFGS algorithm, achieving a proven linear convergence rate for strongly convex and smooth functions and demonstrating strong experimental performance on both convex and non-convex problems with high precision.
We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a recent approach to variance reduction for stochastic gradient descent from Johnson and Zhang (2013). We demonstrate experimentally that our algorithm performs well on large-scale convex and non-convex optimization problems, exhibiting linear convergence and rapidly solving the optimization problems to high levels of precision. Furthermore, we show that our algorithm performs well for a wide-range of step sizes, often differing by several orders of magnitude.