Conference proceeding
Stochastic Optimization for DC Functions and Non-smooth Non-convex Regularizers with Non-asymptotic Convergence
Proceedings of Machine Learning Research, Vol.97, pp.6942-6951
International Conference on Machine Learning, 36th (Long Beach, California, USA, 06/09/2019 - 06/15/2019)
2019
Abstract
Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC functions have been extensively studied, stochastic optimization that is more suitable for learning with big data remains under-explored. In this paper, we propose new stochastic optimization algorithms and study their first-order convergence theories for solving a broad family of DC functions. We improve the existing algorithms and theories of stochastic optimization for DC functions from both practical and theoretical perspectives. Moreover, we extend the proposed stochastic algorithms for DC functions to solve problems with a general non-convex non-differentiable regularizer, which does not necessarily have a DC decomposition but enjoys an efficient proximal mapping. To the best of our knowledge, this is the first work that gives the first non-asymptotic convergence for solving non-convex optimization whose objective has a general non-convex non-differentiable regularizer.
Details
- Title: Subtitle
- Stochastic Optimization for DC Functions and Non-smooth Non-convex Regularizers with Non-asymptotic Convergence
- Creators
- Yi XuQi QiQihang LinRong JinTianbao Yang
- Resource Type
- Conference proceeding
- Publication Details
- Proceedings of Machine Learning Research, Vol.97, pp.6942-6951
- Conference
- International Conference on Machine Learning, 36th (Long Beach, California, USA, 06/09/2019 - 06/15/2019)
- Language
- English
- Date published
- 2019
- Academic Unit
- Computer Science; Business Analytics
- Record Identifier
- 9984259471202771
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