Local Convergence

Local convergence in optimization focuses on analyzing the behavior of algorithms near optimal solutions, aiming to establish convergence rates and conditions for guaranteed convergence. Current research investigates this in various contexts, including gradient descent methods for diverse models like neural networks and min-max games, as well as second-order methods and algorithms operating on Riemannian manifolds. Understanding local convergence is crucial for developing efficient and reliable optimization algorithms across numerous fields, from machine learning and signal processing to control theory and game theory, impacting both theoretical understanding and practical applications.

Papers

October 12, 2024

Anderson Acceleration in Nonsmooth Problems: Local Convergence via Active Manifold Identification
Kexin Li, Luwei Bai, Xiao Wang, Hao Wang
Local Convergence Anderson Acceleration Nonsmooth Dynamical System Nonsmooth Optimization Fixed Point Iteration Accelerated Algorithm

October 11, 2024

Improved Sample Complexity for Global Convergence of Actor-Critic Algorithms
Navdeep Kumar, Priyank Agrawal, Giorgia Ramponi, Kfir Yehuda Levy, Shie Mannor
Practical Algorithm Sample Complexity Convergence Guarantee Global Convergence Local Convergence Gradient Dominance Property

July 29, 2024

Mixed Newton Method for Optimization in Complex Spaces
Nikita Yudin, Roland Hildebrand, Sergey Bakhurin, Alexander Degtyarev, Anna Lisachenko, Ilya Kuruzov, Andrei Semenov, Mohammad Alkousa
Optimization Purpose Regularization Model Complex Valued Local Convergence Newton Method Sharp Minimum

July 14, 2024

Parameter Estimation for Generalized Low-Rank Matrix Sensing by Learning on Riemannian Manifolds
Osbert Bastani
Convergence Guarantee Parameter Estimation Riemannian Manifold Optimal Estimation Local Convergence Matrix Sensing Link Function

June 22, 2024

Efficient Low-rank Identification via Accelerated Iteratively Reweighted Nuclear Norm Minimization
Hao Wang, Ye Wang, Xiangyu Yang
Low Rank Low Rate ACCELERATION Local Convergence Nuclear Norm Low Rank Matrix Estimation Schatten $P$ Norm

June 7, 2024

Gradient Descent on Logistic Regression with Non-Separable Data and Large Step Sizes
Si Yi Meng, Antonio Orvieto, Daniel Yiming Cao, Christopher De Sa
Gradient Descent Logistic Regression Global Convergence Step Size Local Convergence

June 3, 2024

How Does Gradient Descent Learn Features -- A Local Analysis for Regularized Two-Layer Neural Networks
Mo Zhou, Rong Ge
Gradient Descent Gradient Based Neural Tangent Kernel Feature Learning Two Layer Neural Network Local Convergence

May 27, 2024

Convergence of SGD with momentum in the nonconvex case: A time window-based analysis
Junwen Qiu, Bohao Ma, Andre Milzarek
Stochastic Gradient Descent Early Stage Convergence Convergence Analysis Residual Momentum General Nonconvex Local Convergence Convergence Behavior

May 22, 2024

Local convergence of simultaneous min-max algorithms to differential equilibrium on Riemannian manifold
Sixin Zhang
Riemannian Geometry Local Convergence Wasserstein Gan Equilibrium State Stackelberg Equilibrium Differentiable Game

November 26, 2023

Local Convergence of Approximate Newton Method for Two Layer Nonlinear Regression
Zhihang Li, Zhao Song, Zifan Wang, Junze Yin
Large Language Model Softmax Function Local Convergence Layer Regression

October 21, 2023

A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport
Tianyi Lin, Marco Cuturi, Michael I. Jordan
Optimal Transport Local Convergence Interior Point Semismooth Newton

October 11, 2023

Bridging the Gap between Newton-Raphson Method and Regularized Policy Iteration
Zeyang Li, Chuxiong Hu, Yunan Wang, Guojian Zhan, Jie Li, Shengbo Eben Li
Policy Iteration Local Convergence Newton Iteration Soft Actor Critic Algorithm Newton Raphson

September 12, 2023

Convergence of Gradient-based MAML in LQR
Negin Musavi, Geir E. Dullerud
Reinforcement Learning Early Stage Convergence Convergence Guarantee Local Convergence Model Agnostic Meta Learning Quadratic Control

May 31, 2023

On the Linear Convergence of Policy Gradient under Hadamard Parameterization
Jiacai Liu, Jinchi Chen, Ke Wei
Policy Gradient Linear Convergence Local Convergence Hadamard Layer Deterministic Policy Gradient

May 26, 2023

May 14, 2023

Local Convergence of Gradient Descent-Ascent for Training Generative Adversarial Networks
Evan Becker, Parthe Pandit, Sundeep Rangan, Alyson K. Fletcher
Generative Model Generative Adversarial Network GAN Model Generative Adversarial Local Convergence Gradient Descent Ascent

April 18, 2023

Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks
Jing An, Jianfeng Lu
Deep Neural Network Stochastic Gradient Descent Early Stage Convergence Loss Landscape Non Convex Objective Local Convergence

March 3, 2023

Can We Find Nash Equilibria at a Linear Rate in Markov Games?
Zhuoqing Song, Jason D. Lee, Zhuoran Yang
Nash Equilibrium Policy Optimization Markov Game Two Player Zero Sum Local Convergence

November 3, 2022

Geometry and convergence of natural policy gradient methods
Johannes Müller, Guido Montúfar
Markov Decision Process Early Stage Convergence Geometric Analysis Natural Policy Gradient Local Convergence Policy Parametrization

Local Convergence

Papers

Anderson Acceleration in Nonsmooth Problems: Local Convergence via Active Manifold Identification

Improved Sample Complexity for Global Convergence of Actor-Critic Algorithms

Mixed Newton Method for Optimization in Complex Spaces

Parameter Estimation for Generalized Low-Rank Matrix Sensing by Learning on Riemannian Manifolds

Efficient Low-rank Identification via Accelerated Iteratively Reweighted Nuclear Norm Minimization

Gradient Descent on Logistic Regression with Non-Separable Data and Large Step Sizes

How Does Gradient Descent Learn Features -- A Local Analysis for Regularized Two-Layer Neural Networks

Convergence of SGD with momentum in the nonconvex case: A time window-based analysis

Local convergence of simultaneous min-max algorithms to differential equilibrium on Riemannian manifold

Local Convergence of Approximate Newton Method for Two Layer Nonlinear Regression

A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport

Bridging the Gap between Newton-Raphson Method and Regularized Policy Iteration

Convergence of Gradient-based MAML in LQR

On the Linear Convergence of Policy Gradient under Hadamard Parameterization

Local Convergence of Gradient Methods for Min-Max Games: Partial Curvature Generically Suffices

Fast and Accurate Estimation of Low-Rank Matrices from Noisy Measurements via Preconditioned Non-Convex Gradient Descent

Local Convergence of Gradient Descent-Ascent for Training Generative Adversarial Networks

Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks

Can We Find Nash Equilibria at a Linear Rate in Markov Games?

Geometry and convergence of natural policy gradient methods