Timezone: »
Epoch gradient descent method (a.k.a. Epoch-GD) proposed by (Hazan and Kale, 2011) was deemeda breakthrough for stochastic strongly convex minimization, which achieves theoptimal convergence rate of O(1/T) with T iterative updates for the objective gap. However, its extension to solving stochastic min-max problems with strong convexity and strong concavity still remains open, and it is still unclear whethera fast rate ofO(1/T)for theduality gapis achievable for stochastic min-max optimization under strong convexity and strong concavity. Although some re-cent studies have proposed stochastic algorithms with fast convergence rates formin-max problems, they require additional assumptions about the problem, e.g.,smoothness, bi-linear structure, etc. In this paper, we bridge this gap by providinga sharp analysis of epoch-wise stochastic gradient descent ascent method (referredto as Epoch-GDA) for solving strongly convex strongly concave (SCSC) min-maxproblems, without imposing any additional assumption about smoothness or the function’s structure. To the best of our knowledge, our result is the first one that shows Epoch-GDA can achieve the optimal rate ofO(1/T)for the duality gapof general SCSC min-max problems. We emphasize that such generalization of Epoch-GD for strongly convex minimization problems to Epoch-GDA for SCSC min-max problems is non-trivial and requires novel technical analysis. Moreover, we notice that the key lemma can also be used for proving the convergence of Epoch-GDA for weakly-convex strongly-concave min-max problems, leading to a nearly optimal complexity without resorting to smoothness or other structural conditions.
Author Information
Yan Yan (Washington State University)
Yi Xu (Alibaba Group U.S. Inc.)
Qihang Lin (University of Iowa)
Wei Liu (Tencent AI Lab)
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 -
2022 : An Empirical Study on Distribution Shift Robustness From the Perspective of Pre-Training and Data Augmentation »
Ziquan Liu · Yi Xu · Yuanhong Xu · Qi Qian · Hao Li · Rong Jin · Xiangyang Ji · Antoni Chan -
2022 Spotlight: Lightning Talks 6A-4 »
Xiu-Shen Wei · Konstantina Dritsa · Guillaume Huguet · ABHRA CHAUDHURI · Zhenbin Wang · Kevin Qinghong Lin · Yutong Chen · Jianan Zhou · Yongsen Mao · Junwei Liang · Jinpeng Wang · Mao Ye · Yiming Zhang · Aikaterini Thoma · H.-Y. Xu · Daniel Sumner Magruder · Enwei Zhang · Jianing Zhu · Ronglai Zuo · Massimiliano Mancini · Hanxiao Jiang · Jun Zhang · Fangyun Wei · Faen Zhang · Ioannis Pavlopoulos · Zeynep Akata · Xiatian Zhu · Jingfeng ZHANG · Alexander Tong · Mattia Soldan · Chunhua Shen · Yuxin Peng · Liuhan Peng · Michael Wray · Tongliang Liu · Anjan Dutta · Yu Wu · Oluwadamilola Fasina · Panos Louridas · Angel Chang · Manik Kuchroo · Manolis Savva · Shujie LIU · Wei Zhou · Rui Yan · Gang Niu · Liang Tian · Bo Han · Eric Z. XU · Guy Wolf · Yingying Zhu · Brian Mak · Difei Gao · Masashi Sugiyama · Smita Krishnaswamy · Rong-Cheng Tu · Wenzhe Zhao · Weijie Kong · Chengfei Cai · WANG HongFa · Dima Damen · Bernard Ghanem · Wei Liu · Mike Zheng Shou -
2022 Spotlight: Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization »
Wei Jiang · Gang Li · Yibo Wang · Lijun Zhang · Tianbao Yang -
2022 Spotlight: Egocentric Video-Language Pretraining »
Kevin Qinghong Lin · Jinpeng Wang · Mattia Soldan · Michael Wray · Rui Yan · Eric Z. XU · Difei Gao · Rong-Cheng Tu · Wenzhe Zhao · Weijie Kong · Chengfei Cai · WANG HongFa · Dima Damen · Bernard Ghanem · Wei Liu · Mike Zheng Shou -
2022 Spotlight: Lightning Talks 6B-1 »
Yushun Zhang · Duc Nguyen · Jiancong Xiao · Wei Jiang · Yaohua Wang · Yilun Xu · Zhen LI · Anderson Ye Zhang · Ziming Liu · Fangyi Zhang · Gilles Stoltz · Congliang Chen · Gang Li · Yanbo Fan · Ruoyu Sun · Naichen Shi · Yibo Wang · Ming Lin · Max Tegmark · Lijun Zhang · Jue Wang · Ruoyu Sun · Tommi Jaakkola · Senzhang Wang · Zhi-Quan Luo · Xiuyu Sun · Zhi-Quan Luo · Tianbao Yang · Rong Jin -
2022 Spotlight: Lightning Talks 4A-2 »
Barakeel Fanseu Kamhoua · Hualin Zhang · Taiki Miyagawa · Tomoya Murata · Xin Lyu · Yan Dai · Elena Grigorescu · Zhipeng Tu · Lijun Zhang · Taiji Suzuki · Wei Jiang · Haipeng Luo · Lin Zhang · Xi Wang · Young-San Lin · Huan Xiong · Liyu Chen · Bin Gu · Jinfeng Yi · Yongqiang Chen · Sandeep Silwal · Yiguang Hong · Maoyuan Song · Lei Wang · Tianbao Yang · Han Yang · MA Kaili · Samson Zhou · Deming Yuan · Bo Han · Guodong Shi · Bo Li · James Cheng -
2022 Spotlight: Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor »
Lijun Zhang · Wei Jiang · Jinfeng Yi · Tianbao Yang -
2022 Spotlight: Lightning Talks 1B-4 »
Andrei Atanov · Shiqi Yang · Wanshan Li · Yongchang Hao · Ziquan Liu · Jiaxin Shi · Anton Plaksin · Jiaxiang Chen · Ziqi Pan · yaxing wang · Yuxin Liu · Stepan Martyanov · Alessandro Rinaldo · Yuhao Zhou · Li Niu · Qingyuan Yang · Andrei Filatov · Yi Xu · Liqing Zhang · Lili Mou · Ruomin Huang · Teresa Yeo · kai wang · Daren Wang · Jessica Hwang · Yuanhong Xu · Qi Qian · Hu Ding · Michalis Titsias · Shangling Jui · Ajay Sohmshetty · Lester Mackey · Joost van de Weijer · Hao Li · Amir Zamir · Xiangyang Ji · Antoni Chan · Rong Jin -
2022 Spotlight: Improved Fine-Tuning by Better Leveraging Pre-Training Data »
Ziquan Liu · Yi Xu · Yuanhong Xu · Qi Qian · Hao Li · Xiangyang Ji · Antoni Chan · Rong Jin -
2022 Poster: Egocentric Video-Language Pretraining »
Kevin Qinghong Lin · Jinpeng Wang · Mattia Soldan · Michael Wray · Rui Yan · Eric Z. XU · Difei Gao · Rong-Cheng Tu · Wenzhe Zhao · Weijie Kong · Chengfei Cai · WANG HongFa · Dima Damen · Bernard Ghanem · Wei Liu · Mike Zheng Shou -
2022 Poster: Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximization »
Quanqi Hu · YONGJIAN ZHONG · Tianbao Yang -
2022 Poster: ProtoX: Explaining a Reinforcement Learning Agent via Prototyping »
Ronilo Ragodos · Tong Wang · Qihang Lin · Xun Zhou -
2022 Poster: Large-scale Optimization of Partial AUC in a Range of False Positive Rates »
Yao Yao · Qihang Lin · Tianbao Yang -
2022 Poster: Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor »
Lijun Zhang · Wei Jiang · Jinfeng Yi · Tianbao Yang -
2022 Poster: Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization »
Wei Jiang · Gang Li · Yibo Wang · Lijun Zhang · Tianbao Yang -
2022 Poster: Improved Fine-Tuning by Better Leveraging Pre-Training Data »
Ziquan Liu · Yi Xu · Yuanhong Xu · Qi Qian · Hao Li · Xiangyang Ji · Antoni Chan · Rong Jin -
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: Neural Routing by Memory »
Kaipeng Zhang · Zhenqiang Li · Zhifeng Li · Wei Liu · Yoichi Sato -
2021 Poster: Generalized and Discriminative Few-Shot Object Detection via SVD-Dictionary Enhancement »
Aming WU · Suqi Zhao · Cheng Deng · Wei Liu -
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: 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: Towards Playing Full MOBA Games with Deep Reinforcement Learning »
Deheng Ye · Guibin Chen · Wen Zhang · Sheng Chen · Bo Yuan · Bo Liu · Jia Chen · Zhao Liu · Fuhao Qiu · Hongsheng Yu · Yinyuting Yin · Bei Shi · Liang Wang · Tengfei Shi · Qiang Fu · Wei Yang · Lanxiao Huang · Wei Liu -
2020 Poster: Fewer is More: A Deep Graph Metric Learning Perspective Using Fewer Proxies »
Yuehua Zhu · Muli Yang · Cheng Deng · Wei Liu -
2020 Spotlight: Fewer is More: A Deep Graph Metric Learning Perspective Using Fewer Proxies »
Yuehua Zhu · Muli Yang · Cheng Deng · Wei Liu -
2020 Poster: Adversarial Learning for Robust Deep Clustering »
Xu Yang · Cheng Deng · Kun Wei · Junchi Yan · Wei Liu -
2019 Poster: Semantic Conditioned Dynamic Modulation for Temporal Sentence Grounding in Videos »
Yitian Yuan · Lin Ma · Jingwen Wang · Wei Liu · Wenwu Zhu -
2019 Poster: Cross-Modal Learning with Adversarial Samples »
CHAO LI · Shangqian Gao · Cheng Deng · De Xie · Wei Liu -
2019 Poster: Category Anchor-Guided Unsupervised Domain Adaptation for Semantic Segmentation »
Qiming ZHANG · Jing Zhang · Wei Liu · Dacheng Tao -
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: First-order Stochastic Algorithms for Escaping From Saddle Points in Almost Linear Time »
Yi Xu · Rong Jin · Tianbao Yang -
2018 Poster: Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling »
Yunzhe Tao · Qi Sun · Qiang Du · Wei Liu -
2018 Poster: Adaptive Negative Curvature Descent with Applications in Non-convex Optimization »
Mingrui Liu · Zhe Li · Xiaoyu Wang · Jinfeng Yi · Tianbao Yang -
2018 Poster: Generalizing Graph Matching beyond Quadratic Assignment Model »
Tianshu Yu · Junchi Yan · Yilin Wang · Wei Liu · baoxin Li -
2018 Poster: Faster Online Learning of Optimal Threshold for Consistent F-measure Optimization »
Xiaoxuan Zhang · Mingrui Liu · Xun Zhou · Tianbao Yang -
2018 Poster: Deep Non-Blind Deconvolution via Generalized Low-Rank Approximation »
Wenqi Ren · Jiawei Zhang · Lin Ma · Jinshan Pan · Xiaochun Cao · Wangmeng Zuo · Wei Liu · Ming-Hsuan Yang -
2018 Poster: Fast Rates of ERM and Stochastic Approximation: Adaptive to Error Bound Conditions »
Mingrui Liu · Xiaoxuan Zhang · Lijun Zhang · Rong Jin · Tianbao Yang -
2018 Poster: Distilled Wasserstein Learning for Word Embedding and Topic Modeling »
Hongteng Xu · Wenlin Wang · Wei Liu · Lawrence Carin -
2018 Poster: Parsimonious Quantile Regression of Financial Asset Tail Dynamics via Sequential Learning »
Xing Yan · Weizhong Zhang · Lin Ma · Wei Liu · Qi Wu -
2017 Poster: ADMM without a Fixed Penalty Parameter: Faster Convergence with New Adaptive Penalization »
Yi Xu · Mingrui Liu · Qihang Lin · Tianbao Yang -
2017 Poster: Geometric Descent Method for Convex Composite Minimization »
Shixiang Chen · Shiqian Ma · Wei Liu -
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: Mixture-Rank Matrix Approximation for Collaborative Filtering »
Dongsheng Li · Chao Chen · Wei Liu · Tun Lu · Ning Gu · Stephen Chu -
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 -
2014 Poster: Discrete Graph Hashing »
Wei Liu · Cun Mu · Sanjiv Kumar · Shih-Fu Chang -
2014 Spotlight: Discrete Graph Hashing »
Wei Liu · Cun Mu · Sanjiv Kumar · Shih-Fu Chang -
2014 Poster: Zeta Hull Pursuits: Learning Nonconvex Data Hulls »
Yuanjun Xiong · Wei Liu · Deli Zhao · Xiaoou Tang