1 citations · 1 across the 18 of their papers we have counts for
19 papers
Optimal High-Order Methods for Solving Monotone Variational Inequalities
Xinliang Zhang, Lesi Chen, Linxuan Pan +3
We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI). Monteiro and Svaiter (SIAM J. Optim., 2012) showed that a second-order method,…
Randomized Quasi-Gauss--Newton Methods for Solving General Nonlinear Equations
Chengchang Liu, Luo Luo
This paper considers the local convergence for solving general nonlinear equations. We establish randomized quasi-Gauss--Newton methods based on the approximation of the Gram matri…
Halpern Iteration Achieves th-Order Oracle Complexity for Monotone Variational Inequalities
Lesi Chen, Xinliang Zhang, Hengyu Wang +3
We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI). Monteiro and Svaiter (SIAM J. Optim., 2012) showed that a second-order method,…
Optimal Convex Optimization with Inexact Second-Order Oracles
Lesi Chen, Chengchang Liu, Luo Luo +2
In this paper, we present a novel second-order method called Accelerated Inexact Newton Extragradient (AINE) for convex optimization using -inexact Hessians. We show that AINE c…
Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise
Bin Luo, Chengchang Liu, Jonathan Allcock +2
We study stochastic optimization with heavy-tailed gradient noise. We first propose a novel quantum mean estimator for multivariate heavy-tailed random variables that achieves lowe…
On the Convergence of Stochastic Low-Rank Adaptation
Ru Wang, Chengchang Liu, John C. S. Lui
Low-rank adaptation (LoRA) optimizes over two adapters and that form a low-…
Stochastic Non-Smooth Non-Convex Optimization with Decision-Dependent Distributions
Chengchang Liu, Zongqi Wan, Haishan Ye +1
We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are avail…
Second-Order Bilevel Optimization with Accelerated Convergence Rates
Sheng Yang, Chengchang Liu, Lesi Chen +1
This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves…
Solving Convex-Concave Problems with th-Order Oracle Complexity
Lesi Chen, Xinliang Zhang, Chengchang Liu +3
When the objective has Lipschitz continuous th-order derivatives, it is known that convex-concave minimax problems can be solved with th-order ora…
Solving Convex-Concave Problems with Second-Order Oracle Complexity
Lesi Chen, Chengchang Liu, Luo Luo +1
Previous algorithms can solve convex-concave minimax problems with second-order oracle calls usin…
Faster Newton Methods for Convex and Nonconvex Optimization in Gradient Complexity
Lesi Chen, Chengchang Liu, Luo Luo +1
Second-order optimization methods are computationally expensive for large-scale problems. Recently, Doikov, Chayti, and Jaggi (ICML 2023) proposed the LazyCRN method that reduces c…
Quantum Algorithm for Online Exp-concave Optimization
Jianhao He, Chengchang Liu, Xutong Liu +2
We explore whether quantum advantages can be found for the zeroth-order feedback online exp-concave optimization problem, which is also known as bandit exp-concave optimization wit…
Quantum Algorithms for Non-smooth Non-convex Optimization
Chengchang Liu, Chaowen Guan, Jianhao He +1
This paper considers the problem for finding the -Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of imp…
Second-Order Min-Max Optimization with Lazy Hessians
Lesi Chen, Chengchang Liu, Jingzhao Zhang
This paper studies second-order methods for convex-concave minimax optimization. Monteiro and Svaiter (2012) proposed a method to solve the problem with an optimal iteration comple…
Incremental Gauss--Newton Methods with Superlinear Convergence Rates
Zhiling Zhou, Zhuanghua Liu, Chengchang Liu +1
This paper addresses the challenge of solving large-scale nonlinear equations with Hölder continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within e…
Communication Efficient Distributed Newton Method with Fast Convergence Rates
Chengchang Liu, Lesi Chen, Luo Luo +1
We propose a communication and computation efficient second-order method for distributed optimization. For each iteration, our method only requires communication c…
Symmetric Rank- Methods
Chengchang Liu, Cheng Chen, Luo Luo
This paper proposes a novel class of block quasi-Newton methods for convex optimization which we call symmetric rank- (SR-) methods. Each iteration of SR- incorporates the…
Universal Tensor Methods for Monotone Variational Inequalities
Chengchang Liu, John C. S. Lui, Luo Luo
We study monotone variational inequalities whose operators have Hölder continuous higher-order derivatives. For a fixed order , we assume that the -th derivative of…
Quasi-Newton Methods for Saddle Point Problems and Beyond
Chengchang Liu, Luo Luo
This paper studies quasi-Newton methods for solving strongly-convex-strongly-concave saddle point problems (SPP). We propose greedy and random Broyden family updates for SPP, which…