352 citations · 495 across the 43 of their papers we have counts for
46 papers
A counterexample to global convergence of classical DFP under the standard strong Wolfe conditions
Benqi Liu, Zichen Wang, Zaiwen Wen +2
A long-standing open question in quasi-Newton optimization asks whether the classical Davidon--Fletcher--Powell (DFP) method converges globally on uniformly convex objectives when…
On the Optimal Lower and Upper Complexity Bounds for a Class of Composite Optimization Problems
Zhenyuan Zhu, Fan Chen, Junyu Zhang +1
We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem , where is smooth and is convex. Giv…
Monte Carlo Policy Gradient Method for Binary Optimization
Cheng Chen, Ruitao Chen, Tianyou Li +2
Binary optimization has a wide range of applications in combinatorial optimization problems such as MaxCut, MIMO detection, and MaxSAT. However, these problems are typically NP-har…
The Error in Multivariate Linear Extrapolation with Applications to Derivative-Free Optimization
Liyuan Cao, Zaiwen Wen, Ya-xiang Yuan
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. Howeve…
Convergence Analysis of Stochastic Gradient Descent with MCMC Estimators
Tianyou Li, Fan Chen, Huajie Chen +1
Understanding stochastic gradient descent (SGD) and its variants is essential for machine learning. However, most of the preceding analyses are conducted under amenable conditions…
Gauss-Newton Temporal Difference Learning with Nonlinear Function Approximation
Zhifa Ke, Junyu Zhang, Zaiwen Wen
In this paper, a Gauss-Newton Temporal Difference (GNTD) learning method is proposed to solve the Q-learning problem with nonlinear function approximation. In each iteration, our m…
On the local convergence of the semismooth Newton method for composite optimization
Jiang Hu, Tonghua Tian, Shaohua Pan +1
In this paper, we consider a large class of nonlinear equations derived from first-order type methods for solving composite optimization problems. Traditional approaches to establi…
Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation
Liyuan Cao, Zaiwen Wen, Ya-xiang Yuan
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are…
A Unified Primal-Dual Algorithm Framework for Inequality Constrained Problems
Zhenyuan Zhu, Fan Chen, Junyu Zhang +1
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The…
Riemannian Natural Gradient Methods
Jiang Hu, Ruicheng Ao, Anthony Man-Cho So +2
This paper studies large-scale optimization problems on Riemannian manifolds whose objective function is a finite sum of negative log-probability losses. Such problems arise in var…
A Near-Optimal Primal-Dual Method for Off-Policy Learning in CMDP
Fan Chen, Junyu Zhang, Zaiwen Wen
As an important framework for safe Reinforcement Learning, the Constrained Markov Decision Process (CMDP) has been extensively studied in the recent literature. However, despite th…
A Decomposition Augmented Lagrangian Method for Low-rank Semidefinite Programming
Yifei Wang, Kangkang Deng, Haoyang Liu +1
We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functi…
NG+ : A Multi-Step Matrix-Product Natural Gradient Method for Deep Learning
Minghan Yang, Dong Xu, Qiwen Cui +2
In this paper, a novel second-order method called NG+ is proposed. By following the rule ``the shape of the gradient equals the shape of the parameter", we define a generalized fis…
A Stochastic Composite Augmented Lagrangian Method For Reinforcement Learning
Yongfeng Li, Mingming Zhao, Weijie Chen +1
In this paper, we consider the linear programming (LP) formulation for deep reinforcement learning. The number of the constraints depends on the size of state and action spaces, wh…
Joint Bandwidth Allocation and Path Selection in WANs with Path Cardinality Constraints
Jinxin Wang, Fan Zhang, Zhonglin Xie +2
In this paper, we study a joint bandwidth allocation and path selection problem via solving a multi-objective minimization problem under the path cardinality constraints, namely MO…
On the Analysis of Model-free Methods for the Linear Quadratic Regulator
Zeyu Jin, Johann Michael Schmitt, Zaiwen Wen
Many reinforcement learning methods achieve great success in practice but lack theoretical foundation. In this paper, we study the convergence analysis on the problem of the Linear…
Enhance Curvature Information by Structured Stochastic Quasi-Newton Methods
Minghan Yang, Dong Xu, Hongyu Chen +2
In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to i…
Sketchy Empirical Natural Gradient Methods for Deep Learning
Minghan Yang, Dong Xu, Zaiwen Wen +2
In this paper, we develop an efficient sketchy empirical natural gradient method (SENG) for large-scale deep learning problems. The empirical Fisher information matrix is usually l…
A Trust-Region Method For Nonsmooth Nonconvex Optimization
Ziang Chen, Andre Milzarek, Zaiwen Wen
We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a (probably nonconvex) smooth function…
A Stochastic Trust-Region Framework for Policy Optimization
Mingming Zhao, Yongfeng Li, Zaiwen Wen
In this paper, we study a few challenging theoretical and numerical issues on the well known trust region policy optimization for deep reinforcement learning. The goal is to find a…
A Stochastic Extra-Step Quasi-Newton Method for Nonsmooth Nonconvex Optimization
Minghan Yang, Andre Milzarek, Zaiwen Wen +1
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient o…
On The Geometric Analysis of A Quartic-quadratic Optimization Problem under A Spherical Constraint
Haixiang Zhang, Andre Milzarek, Zaiwen Wen +1
This paper considers the problem of solving a special quartic-quadratic optimization problem with a single sphere constraint, namely, finding a global and local minimizer of $\frac…
Ground states and their characterization of spin- Bose-Einstein condensates
Tonghua Tian, Yongyong Cai, Xinming Wu +1
The computation of the ground states of spin- Bose-Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize…
An exact penalty approach for optimization with nonnegative orthogonality constraints
Bo Jiang, Xiang Meng, Zaiwen Wen +1
Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the const…