An Inexact Variable Metric Proximal Point Algorithm for Generic Quasi-Newton Acceleration
This work addresses optimization efficiency for machine learning practitioners dealing with large-scale, high-dimensional problems, representing an incremental advancement by combining existing techniques like SVRG and BFGS.
The authors tackled the problem of accelerating gradient-based optimization algorithms by proposing QNing, an inexact variable-metric proximal point algorithm, which achieved significant improvements in training machine learning methods on large, high-dimensional datasets.
We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic variance-reduced gradient descent algorithm (SVRG) and other randomized incremental optimization algorithms. QNing is also compatible with composite objectives, meaning that it has the ability to provide exactly sparse solutions when the objective involves a sparsity-inducing regularization. When combined with limited-memory BFGS rules, QNing is particularly effective to solve high-dimensional optimization problems, while enjoying a worst-case linear convergence rate for strongly convex problems. We present experimental results where QNing gives significant improvements over competing methods for training machine learning methods on large samples and in high dimensions.