183 citations · 474 across the 30 of their papers we have counts for
18 papers · 1 filter
Tight Complexity of Muon under Heavy-Tailed Noise
Jiayu Zhang, Tianyi Lin
A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized. The layerwise input-output structure of neural networks mot…
Perseus: A Simple and Optimal High-Order Method for Variational Inequalities
Tianyi Lin, Michael. I. Jordan
This paper settles an open and challenging question pertaining to the design of simple and optimal high-order methods for solving smooth and monotone variational inequalities (VIs)…
Monotone Inclusions, Acceleration and Closed-Loop Control
Tianyi Lin, Michael. I. Jordan
We propose and analyze a new dynamical system with a closed-loop control law in a Hilbert space , aiming to shed light on the acceleration phenomenon for \textit{monot…
Finite-Time Last-Iterate Convergence for Multi-Agent Learning in Games
Tianyi Lin, Zhengyuan Zhou, Panayotis Mertikopoulos +1
In this paper, we consider multi-agent learning via online gradient descent in a class of games called -cocoercive games, a fairly broad class of games that admits many Nash equ…
Near-Optimal Algorithms for Minimax Optimization
Tianyi Lin, Chi Jin, Michael. I. Jordan
This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. C…
A Control-Theoretic Perspective on Optimal High-Order Optimization
Tianyi Lin, Michael. I. Jordan
We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $Φ: \mathbb{R}^d…
A Unified Adaptive Tensor Approximation Scheme to Accelerate Composite Convex Optimization
Bo Jiang, Tianyi Lin, Shuzhong Zhang
In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization mo…
Improved Sample Complexity for Stochastic Compositional Variance Reduced Gradient
Tianyi Lin, Chenyou Fan, Mengdi Wang +1
Convex composition optimization is an emerging topic that covers a wide range of applications arising from stochastic optimal control, reinforcement learning and multi-stage stocha…
An ADMM-Based Interior-Point Method for Large-Scale Linear Programming
Tianyi Lin, Shiqian Ma, Yinyu Ye +1
We propose a new framework to implement interior point method (IPM) to solve very large linear programs (LP). Traditional IPMs typically use Newton's method to approximately solve…
Improved Oracle Complexity of Variance Reduced Methods for Nonsmooth Convex Stochastic Composition Optimization
Tianyi Lin, Chenyou Fan, Mengdi Wang
We consider the nonsmooth convex composition optimization problem where the objective is a composition of two finite-sum functions and analyze stochastic compositional variance red…
A Unified Scheme to Accelerate Adaptive Cubic Regularization and Gradient Methods for Convex Optimization
Bo Jiang, Tianyi Lin, Shuzhong Zhang
In this paper we propose a unified two-phase scheme for convex optimization to accelerate: (1) the adaptive cubic regularization methods with exact/inexact Hessian matrices, and (2…
Structured Nonconvex and Nonsmooth Optimization: Algorithms and Iteration Complexity Analysis
Bo Jiang, Tianyi Lin, Shiqian Ma +1
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a techn…
Distributed Linearized Alternating Direction Method of Multipliers for Composite Convex Consensus Optimization
Necdet Serhat Aybat, Zi Wang, Tianyi Lin +1
Given an undirected graph of agents connected with edges in , we study how to compute an optimal d…
Iteration Complexity Analysis of Multi-Block ADMM for a Family of Convex Minimization without Strong Convexity
Tianyi Lin, Shiqian Ma, Shuzhong Zhang
The alternating direction method of multipliers (ADMM) is widely used in solving structured convex optimization problems due to its superior practical performance. On the theoretic…
Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems
Tianyi Lin, Shiqian Ma, Shuzhong Zhang
The alternating direction method of multipliers (ADMM) has been successfully applied to solve structured convex optimization problems due to its superior practical performance. The…
On the Global Linear Convergence of the ADMM with Multi-Block Variables
Tianyi Lin, Shiqian Ma, Shuzhong Zhang
The alternating direction method of multipliers (ADMM) has been widely used for solving structured convex optimization problems. In particular, the ADMM can solve convex programs t…
On the Sublinear Convergence Rate of Multi-Block ADMM
Tianyi Lin, Shiqian Ma, Shuzhong Zhang
The alternating direction method of multipliers (ADMM) is widely used in solving structured convex optimization problems. Despite of its success in practice, the convergence proper…
An Extragradient-Based Alternating Direction Method for Convex Minimization
Tianyi Lin, Shiqian Ma, Shuzhong Zhang
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually…