183 citations · 474 across the 30 of their papers we have counts for
31 papers
The Row Normalization Puzzle in Muon
Jiayu Zhang, Tianyi Lin
This paper examines how row-wise renormalization affects Muon, focusing on the gap between NorMuon's worst-case guarantees and its practical performance (Li et al.). Despite its gr…
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…
Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization
Yaodong Yu, Tianyi Lin, Eric Mazumdar +1
Distributionally robust supervised learning (DRSL) is emerging as a key paradigm for building reliable machine learning systems for real-world applications -- reflecting the need f…
A Variational Inequality Approach to Bayesian Regression Games
Wenshuo Guo, Michael I. Jordan, Tianyi Lin
Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian…
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…
On the Complexity of Approximating Multimarginal Optimal Transport
Tianyi Lin, Nhat Ho, Marco Cuturi +1
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $…
On the Efficiency of Entropic Regularized Algorithms for Optimal Transport
Tianyi Lin, Nhat Ho, Michael I. Jordan
We present several new complexity results for the entropic regularized algorithms that approximately solve the optimal transport (OT) problem between two discrete probability measu…
On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems
Tianyi Lin, Chi Jin, Michael I. Jordan
We consider nonconvex-concave minimax problems, , where is nonconvex in but concave…
On Structured Filtering-Clustering: Global Error Bound and Optimal First-Order Algorithms
Nhat Ho, Tianyi Lin, Michael I. Jordan
The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields…
On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms
Tianyi Lin, Nhat Ho, Michael I. Jordan
We provide theoretical analyses for two algorithms that solve the regularized optimal transport (OT) problem between two discrete probability measures with at most atoms. We sh…
Sparsemax and Relaxed Wasserstein for Topic Sparsity
Tianyi Lin, Zhiyue Hu, Xin Guo
Topic sparsity refers to the observation that individual documents usually focus on several salient topics instead of covering a wide variety of topics, and a real topic adopts a n…
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…
On the Iteration Complexity Analysis of Stochastic Primal-Dual Hybrid Gradient Approach with High Probability
Linbo Qiao, Tianyi Lin, Qi Qin +1
In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG) approach for solving a wide spectrum of regularized stochastic minimization problems, where the regulariza…
An Incremental Path-Following Splitting Method for Linearly Constrained Nonconvex Nonsmooth Programs
Linbo Qiao, Wei Liu, Steven Hoi
The stationary point of Problem 2 is NOT the stationary point of Problem 1. We are sorry and we are working on fixing this error.
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…
Stochastic Primal-Dual Proximal ExtraGradient Descent for Compositely Regularized Optimization
Tianyi Lin, Linbo Qiao, Teng Zhang +2
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abs…
Relaxed Wasserstein with Applications to GANs
Xin Guo, Johnny Hong, Tianyi Lin +1
Wasserstein Generative Adversarial Networks (WGANs) provide a versatile class of models, which have attracted great attention in various applications. However, this framework has t…