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On the Convergence of Policy in Unregularized Policy Mirror Descent
Dachao Lin, Zhihua Zhang
In this short note, we give the convergence analysis of the policy in the recent famous policy mirror descent (PMD). We mainly consider the unregularized setting following [11] wit…
Explicit Superlinear Convergence Rates of Broyden's Methods in Nonlinear Equations
Dachao Lin, Haishan Ye, Zhihua Zhang
In this paper, we study the explicit superlinear convergence rates of quasi-Newton methods. We particularly focus on the classical Broyden's method for solving nonlinear equations.…
Explicit Superlinear Convergence Rates of The SR1 Algorithm
Haishan Ye, Dachao Lin, Zhihua Zhang +1
We study the convergence rate of the famous Symmetric Rank-1 (SR1) algorithm which has wide applications in different scenarios. Although it has been extensively investigated, SR1…
Near Optimal Stochastic Algorithms for Finite-Sum Unbalanced Convex-Concave Minimax Optimization
Luo Luo, Guangzeng Xie, Tong Zhang +1
This paper considers stochastic first-order algorithms for convex-concave minimax problems of the form , where can be presented by the…
Explicit Convergence Rates of Greedy and Random Quasi-Newton Methods
Dachao Lin, Haishan Ye, Zhihua Zhang
Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In…
Lower Complexity Bounds of Finite-Sum Optimization Problems: The Results and Construction
Yuze Han, Guangzeng Xie, Zhihua Zhang
In this paper, we study the lower complexity bounds for finite-sum optimization problems, where the objective is the average of individual component functions. We consider Prox…
Delayed Projection Techniques for Linearly Constrained Problems: Convergence Rates, Acceleration, and Applications
Xiang Li, Zhihua Zhang
In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machi…
A General Analysis Framework of Lower Complexity Bounds for Finite-Sum Optimization
Guangzeng Xie, Luo Luo, Zhihua Zhang
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of individual smooth convex functions. We consider the algori…
Revisiting Sub-sampled Newton Methods
Haishan Ye, Luo Luo, Zhihua Zhang
Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due…