Timezone: »
Poster
Fast Rates of ERM and Stochastic Approximation: Adaptive to Error Bound Conditions
Mingrui Liu · Xiaoxuan Zhang · Lijun Zhang · Rong Jin · Tianbao Yang
Error bound conditions (EBC) are properties that characterize the growth of an objective function when a point is moved away from the optimal set. They have recently received increasing attention in the field of optimization for developing optimization algorithms with fast convergence. However, the studies of EBC in statistical learning are hitherto still limited. The main contributions of this paper are two-fold. First, we develop fast and intermediate rates of empirical risk minimization (ERM) under EBC for risk minimization with Lipschitz continuous, and smooth convex random functions. Second, we establish fast and intermediate rates of an efficient stochastic approximation (SA) algorithm for risk minimization with Lipschitz continuous random functions, which requires only one pass of $n$ samples and adapts to EBC. For both approaches, the convergence rates span a full spectrum between $\widetilde O(1/\sqrt{n})$ and $\widetilde O(1/n)$ depending on the power constant in EBC, and could be even faster than $O(1/n)$ in special cases for ERM. Moreover, these convergence rates are automatically adaptive without using any knowledge of EBC. Overall, this work not only strengthens the understanding of ERM for statistical learning but also brings new fast stochastic algorithms for solving a broad range of statistical learning problems.
Author Information
Mingrui Liu (The University of Iowa)
Xiaoxuan Zhang (University of Iowa)
Lijun Zhang (Nanjing University (NJU))
Rong Jin (Alibaba)
Tianbao Yang (The University of Iowa)
More from the Same Authors
-
2021 : Practice-Consistent Analysis of Adam-Style Methods »
Zhishuai Guo · Yi Xu · Wotao Yin · Rong Jin · Tianbao Yang -
2021 : A Stochastic Momentum Method for Min-max Bilevel Optimization »
Quanqi Hu · Bokun Wang · Tianbao Yang -
2021 : A Unified DRO View of Multi-class Loss Functions with top-N Consistency »
Dixian Zhu · Tianbao Yang -
2021 : Deep AUC Maximization for Medical Image Classification: Challenges and Opportunities »
Tianbao Yang -
2021 Poster: Simple Stochastic and Online Gradient Descent Algorithms for Pairwise Learning »
ZHENHUAN YANG · Yunwen Lei · Puyu Wang · Tianbao Yang · Yiming Ying -
2021 Poster: Revisiting Smoothed Online Learning »
Lijun Zhang · Wei Jiang · Shiyin Lu · Tianbao Yang -
2021 Poster: Dual Adaptivity: A Universal Algorithm for Minimizing the Adaptive Regret of Convex Functions »
Lijun Zhang · Guanghui Wang · Wei-Wei Tu · Wei Jiang · Zhi-Hua Zhou -
2021 Poster: Stochastic Optimization of Areas Under Precision-Recall Curves with Provable Convergence »
Qi Qi · Youzhi Luo · Zhao Xu · Shuiwang Ji · Tianbao Yang -
2021 Poster: Online Convex Optimization with Continuous Switching Constraint »
Guanghui Wang · Yuanyu Wan · Tianbao Yang · Lijun Zhang -
2021 Poster: An Online Method for A Class of Distributionally Robust Optimization with Non-convex Objectives »
Qi Qi · Zhishuai Guo · Yi Xu · Rong Jin · Tianbao Yang -
2020 Poster: Dynamic Regret of Convex and Smooth Functions »
Peng Zhao · Yu-Jie Zhang · Lijun Zhang · Zhi-Hua Zhou -
2020 Poster: Improved Schemes for Episodic Memory-based Lifelong Learning »
Yunhui Guo · Mingrui Liu · Tianbao Yang · Tajana S Rosing -
2020 Spotlight: Improved Schemes for Episodic Memory-based Lifelong Learning »
Yunhui Guo · Mingrui Liu · Tianbao Yang · Tajana S Rosing -
2020 Poster: A Decentralized Parallel Algorithm for Training Generative Adversarial Nets »
Mingrui Liu · Wei Zhang · Youssef Mroueh · Xiaodong Cui · Jarret Ross · Tianbao Yang · Payel Das -
2020 Poster: Optimal Epoch Stochastic Gradient Descent Ascent Methods for Min-Max Optimization »
Yan Yan · Yi Xu · Qihang Lin · Wei Liu · Tianbao Yang -
2019 Poster: XNAS: Neural Architecture Search with Expert Advice »
Niv Nayman · Asaf Noy · Tal Ridnik · Itamar Friedman · Rong Jin · Lihi Zelnik -
2019 Poster: Non-asymptotic Analysis of Stochastic Methods for Non-Smooth Non-Convex Regularized Problems »
Yi Xu · Rong Jin · Tianbao Yang -
2019 Poster: Stagewise Training Accelerates Convergence of Testing Error Over SGD »
Zhuoning Yuan · Yan Yan · Rong Jin · Tianbao Yang -
2018 : Poster spotlight »
Tianbao Yang · Pavel Dvurechenskii · Panayotis Mertikopoulos · Hugo Berard -
2018 Poster: Adaptive Online Learning in Dynamic Environments »
Lijun Zhang · Shiyin Lu · Zhi-Hua Zhou -
2018 Poster: First-order Stochastic Algorithms for Escaping From Saddle Points in Almost Linear Time »
Yi Xu · Rong Jin · Tianbao Yang -
2018 Poster: Adaptive Negative Curvature Descent with Applications in Non-convex Optimization »
Mingrui Liu · Zhe Li · Xiaoyu Wang · Jinfeng Yi · Tianbao Yang -
2018 Poster: Faster Online Learning of Optimal Threshold for Consistent F-measure Optimization »
Xiaoxuan Zhang · Mingrui Liu · Xun Zhou · Tianbao Yang -
2018 Poster: $\ell_1$-regression with Heavy-tailed Distributions »
Lijun Zhang · Zhi-Hua Zhou -
2017 Poster: ADMM without a Fixed Penalty Parameter: Faster Convergence with New Adaptive Penalization »
Yi Xu · Mingrui Liu · Qihang Lin · Tianbao Yang -
2017 Poster: Scalable Demand-Aware Recommendation »
Jinfeng Yi · Cho-Jui Hsieh · Kush Varshney · Lijun Zhang · Yao Li -
2017 Poster: Improved Dynamic Regret for Non-degenerate Functions »
Lijun Zhang · Tianbao Yang · Jinfeng Yi · Rong Jin · Zhi-Hua Zhou -
2017 Poster: Adaptive Accelerated Gradient Converging Method under H\"{o}lderian Error Bound Condition »
Mingrui Liu · Tianbao Yang -
2017 Poster: Adaptive SVRG Methods under Error Bound Conditions with Unknown Growth Parameter »
Yi Xu · Qihang Lin · Tianbao Yang -
2017 Poster: Learning with Feature Evolvable Streams »
Bo-Jian Hou · Lijun Zhang · Zhi-Hua Zhou -
2016 Poster: Homotopy Smoothing for Non-Smooth Problems with Lower Complexity than $O(1/\epsilon)$ »
Yi Xu · Yan Yan · Qihang Lin · Tianbao Yang -
2016 Poster: Improved Dropout for Shallow and Deep Learning »
Zhe Li · Boqing Gong · Tianbao Yang -
2013 Poster: Mixed Optimization for Smooth Functions »
Mehrdad Mahdavi · Lijun Zhang · Rong Jin -
2013 Poster: Linear Convergence with Condition Number Independent Access of Full Gradients »
Lijun Zhang · Mehrdad Mahdavi · Rong Jin