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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.
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An adaptive half-space projection method for stochastic optimization problems with group sparse regularization
Optimization problems with group sparse regularization are ubiquitous in various popular downstream applications, such as feature selection and compression for Deep Neural Networks (DNNs). Nonetheless, the existing methods in the literature do not perform particularly well when such regularization is used in combination with a stochastic loss function. In particular, it is challenging to design a computationally efficient algorithm with a convergence guarantee and can compute group-sparse solutions. Recently, a half-space stochastic projected gradient ({\tt HSPG}) method was proposed that partly addressed these challenges. This paper presents a substantially enhanced version of {\tt HSPG} that we call~{\tt AdaHSPG+} that makes two noticeable advances. First, {\tt AdaHSPG+} is shown to have a stronger convergence result under significantly looser assumptions than those required by {\tt HSPG}. This improvement in convergence is achieved by integrating variance reduction techniques with a new adaptive strategy for iteratively predicting the support of a solution. Second, {\tt AdaHSPG+} requires significantly less parameter tuning compared to {\tt HSPG}, thus making it more practical and user-friendly. This advance is achieved by designing automatic and adaptive strategies for choosing the type of step employed at each iteration and for updating key hyperparameters. The numerical effectiveness of our proposed {\tt AdaHSPG+} algorithm is demonstrated on both convex and non-convex benchmark problems. The source code is available at \url{https://github.com/tianyic/adahspg}.
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- Award ID(s):
- 2012243
- PAR ID:
- 10432174
- Date Published:
- Journal Name:
- Transactions on machine learning research
- ISSN:
- 2835-8856
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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