Timezone: »
Error bound, an inherent property of an optimization problem, has recently revived in the development of algorithms with improved global convergence without strong convexity. The most studied error bound is the quadratic error bound, which generalizes strong convexity and is satisfied by a large family of machine learning problems. Quadratic error bound have been leveraged to achieve linear convergence in many first-order methods including the stochastic variance reduced gradient (SVRG) method, which is one of the most important stochastic optimization methods in machine learning. However, the studies along this direction face the critical issue that the algorithms must depend on an unknown growth parameter (a generalization of strong convexity modulus) in the error bound. This parameter is difficult to estimate exactly and the algorithms choosing this parameter heuristically do not have theoretical convergence guarantee. To address this issue, we propose novel SVRG methods that automatically search for this unknown parameter on the fly of optimization while still obtain almost the same convergence rate as when this parameter is known. We also analyze the convergence property of SVRG methods under H\"{o}lderian error bound, which generalizes the quadratic error bound.
Author Information
Yi Xu (The University of Iowa)
Qihang Lin (University of Iowa)
Tianbao Yang (The University of Iowa)
More from the Same Authors
-
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: 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: Fast Rates of ERM and Stochastic Approximation: Adaptive to Error Bound Conditions »
Mingrui Liu · Xiaoxuan Zhang · Lijun Zhang · Rong Jin · Tianbao Yang -
2017 Poster: ADMM without a Fixed Penalty Parameter: Faster Convergence with New Adaptive Penalization »
Yi Xu · Mingrui Liu · Qihang Lin · Tianbao Yang -
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 -
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
