Timezone: »
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.
Author Information
Yi Xu (The University of Iowa)
Qi Qi (The University of Iowa)
Qihang Lin (Univ Iowa)
rong jin (alibaba group)
Tianbao Yang (The University of Iowa)
Related Events (a corresponding poster, oral, or spotlight)
-
2019 Oral: Stochastic Optimization for DC Functions and Non-smooth Non-convex Regularizers with Non-asymptotic Convergence »
Wed Jun 12th 10:10 -- 10:15 PM Room Room 104
More from the Same Authors
-
2020 Poster: Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks »
Zhishuai Guo · Mingrui Liu · Zhuoning Yuan · Li Shen · Wei Liu · Tianbao Yang -
2020 Poster: Transparency Promotion with Model-Agnostic Linear Competitors »
Hassan Rafique · Tong Wang · Qihang Lin · Arshia Singhani -
2020 Poster: Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints »
Runchao Ma · Qihang Lin · Tianbao Yang -
2020 Poster: Stochastic Optimization for Non-convex Inf-Projection Problems »
Yan Yan · Yi Xu · Lijun Zhang · Wang Xiaoyu · Tianbao Yang -
2019 Poster: On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization »
Hao Yu · rong jin · Sen Yang -
2019 Poster: On the Computation and Communication Complexity of Parallel SGD with Dynamic Batch Sizes for Stochastic Non-Convex Optimization »
Hao Yu · rong jin -
2019 Oral: On the Computation and Communication Complexity of Parallel SGD with Dynamic Batch Sizes for Stochastic Non-Convex Optimization »
Hao Yu · rong jin -
2019 Oral: On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization »
Hao Yu · rong jin · Sen Yang -
2019 Poster: Katalyst: Boosting Convex Katayusha for Non-Convex Problems with a Large Condition Number »
Zaiyi Chen · Yi Xu · Haoyuan Hu · Tianbao Yang -
2019 Oral: Katalyst: Boosting Convex Katayusha for Non-Convex Problems with a Large Condition Number »
Zaiyi Chen · Yi Xu · Haoyuan Hu · Tianbao Yang -
2018 Poster: Dynamic Regret of Strongly Adaptive Methods »
Lijun Zhang · Tianbao Yang · rong jin · Zhi-Hua Zhou -
2018 Poster: SADAGRAD: Strongly Adaptive Stochastic Gradient Methods »
Zaiyi Chen · Yi Xu · Enhong Chen · Tianbao Yang -
2018 Poster: Level-Set Methods for Finite-Sum Constrained Convex Optimization »
Qihang Lin · Runchao Ma · Tianbao Yang -
2018 Oral: Level-Set Methods for Finite-Sum Constrained Convex Optimization »
Qihang Lin · Runchao Ma · Tianbao Yang -
2018 Oral: SADAGRAD: Strongly Adaptive Stochastic Gradient Methods »
Zaiyi Chen · Yi Xu · Enhong Chen · Tianbao Yang -
2018 Oral: Dynamic Regret of Strongly Adaptive Methods »
Lijun Zhang · Tianbao Yang · rong jin · Zhi-Hua Zhou -
2018 Poster: Fast Stochastic AUC Maximization with $O(1/n)$-Convergence Rate »
Mingrui Liu · Xiaoxuan Zhang · Zaiyi Chen · Xiaoyu Wang · Tianbao Yang -
2018 Oral: Fast Stochastic AUC Maximization with $O(1/n)$-Convergence Rate »
Mingrui Liu · Xiaoxuan Zhang · Zaiyi Chen · Xiaoyu Wang · Tianbao Yang -
2017 Poster: Stochastic Convex Optimization: Faster Local Growth Implies Faster Global Convergence »
Yi Xu · Qihang Lin · Tianbao Yang -
2017 Poster: A Richer Theory of Convex Constrained Optimization with Reduced Projections and Improved Rates »
Tianbao Yang · Qihang Lin · Lijun Zhang -
2017 Talk: A Richer Theory of Convex Constrained Optimization with Reduced Projections and Improved Rates »
Tianbao Yang · Qihang Lin · Lijun Zhang -
2017 Talk: Stochastic Convex Optimization: Faster Local Growth Implies Faster Global Convergence »
Yi Xu · Qihang Lin · Tianbao Yang
