Author name cluster

Qunwei Li

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

4 papers

2 author rows

TMLR Journal 2023 Journal Article

A Cubic Regularization Approach for Finding Local Minimax Points in Nonconvex Minimax Optimization

Ziyi Chen
Zhengyang Hu
Qunwei Li
Zhe Wang
Yi Zhou

Gradient descent-ascent (GDA) is a widely used algorithm for minimax optimization. However, GDA has been proved to converge to stationary points for nonconvex minimax optimization, which are suboptimal compared with local minimax points. In this work, we develop cubic regularization (CR) type algorithms that globally converge to local minimax points in nonconvex-strongly-concave minimax optimization. We first show that local minimax points are equivalent to second-order stationary points of a certain envelope function. Then, inspired by the classic cubic regularization algorithm, we propose an algorithm named Cubic-LocalMinimax for finding local minimax points, and provide a comprehensive convergence analysis by leveraging its intrinsic potential function. Specifically, we establish the global convergence of Cubic-LocalMinimax to a local minimax point at a sublinear convergence rate and characterize its iteration complexity. Also, we propose a GDA-based solver for solving the cubic subproblem involved in Cubic-LocalMinimax up to certain pre-defined accuracy, and analyze the overall gradient and Hessian-vector product computation complexities of such an inexact Cubic-LocalMinimax algorithm. Moreover, we propose a stochastic variant of Cubic-LocalMinimax for large-scale minimax optimization, and characterize its sample complexity under stochastic sub-sampling. Experimental results demonstrate faster or comparable convergence speed of our stochastic Cubic-LocalMinimax than the state-of-the-art algorithms such as GDA and Minimax Cubic-Newton. In particular, our stochastic Cubic-LocalMinimax was also faster as compared to several other algorithms for minimax optimization on a particular adversarial loss for training a convolutional neural network on MNIST.

PDF Details

AAAI Conference 2021 Conference Paper

Learning Graph Neural Networks with Approximate Gradient Descent

Qunwei Li
Shaofeng Zou
Wenliang Zhong

The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached to nodes or graphs. A comprehensive framework for designing and analyzing convergence of GNN training algorithms is developed. The algorithm proposed is applicable to a wide range of activation functions including ReLU, Leaky ReLU, Sigmod, Softplus and Swish. It is shown that the proposed algorithm guarantees a linear convergence rate to the underlying true parameters of GNNs. For both types of GNNs, sample complexity in terms of the number of nodes or the number of graphs is characterized. The impact of feature dimension and GNN structure on the convergence rate is also theoretically characterized. Numerical experiments are further provided to validate our theoretical analysis.

PDF Details

NeurIPS Conference 2020 Conference Paper

A Statistical Mechanics Framework for Task-Agnostic Sample Design in Machine Learning

Bhavya Kailkhura
Jayaraman Thiagarajan
Qunwei Li
Jize Zhang
Yi Zhou
Timo Bremer

In this paper, we present a statistical mechanics framework to understand the effect of sampling properties of training data on the generalization gap of machine learning (ML) algorithms. We connect the generalization gap to the spatial properties of a sample design characterized by the pair correlation function (PCF). In particular, we express generalization gap in terms of the power spectra of the sample design and that of the function to be learned. Using this framework, we show that space-filling sample designs, such as blue noise and Poisson disk sampling, which optimize spectral properties, outperform random designs in terms of the generalization gap and characterize this gain in a closed-form. Our analysis also sheds light on design principles for constructing optimal task-agnostic sample designs that minimize the generalization gap. We corroborate our findings using regression experiments with neural networks on: a) synthetic functions, and b) a complex scientific simulator for inertial confinement fusion (ICF).

PDF Details

ICML Conference 2017 Conference Paper

Convergence Analysis of Proximal Gradient with Momentum for Nonconvex Optimization

Qunwei Li
Yi Zhou 0017
Yingbin Liang
Pramod K. Varshney

In this work, we investigate the accelerated proximal gradient method for nonconvex programming (APGnc). The method compares between a usual proximal gradient step and a linear extrapolation step, and accepts the one that has a lower function value to achieve a monotonic decrease. In specific, under a general nonsmooth and nonconvex setting, we provide a rigorous argument to show that the limit points of the sequence generated by APGnc are critical points of the objective function. Then, by exploiting the Kurdyka-Lojasiewicz (KL) property for a broad class of functions, we establish the linear and sub-linear convergence rates of the function value sequence generated by APGnc. We further propose a stochastic variance reduced APGnc (SVRG-APGnc), and establish its linear convergence under a special case of the KL property. We also extend the analysis to the inexact version of these methods and develop an adaptive momentum strategy that improves the numerical performance.

Details