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06/29/2023
Curvature-Independent Last-Iterate Convergence for Games on Riemannian Manifolds
Numerous applications in machine learning and data analytics can be form...
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02/16/2023
Deterministic Nonsmooth Nonconvex Optimization
We study the complexity of optimizing nonsmooth nonconvex Lipschitz func...
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10/23/2022
Explicit Second-Order Min-Max Optimization Methods with Optimal Convergence Guarantee
We propose and analyze exact and inexact regularized Newton-type methods...
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09/26/2022
On the Complexity of Deterministic Nonsmooth and Nonconvex Optimization
In this paper, we present several new results on minimizing a nonsmooth ...
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09/12/2022
Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization
Nonsmooth nonconvex optimization problems broadly emerge in machine lear...
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07/04/2022
Understanding Performance of Long-Document Ranking Models through Comprehensive Evaluation and Leaderboarding
We carry out a comprehensive evaluation of 13 recent models for ranking ...
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06/09/2022
A Continuous-Time Perspective on Optimal Methods for Monotone Equation Problems
We study rescaled gradient dynamical systems in a Hilbert space ℋ, where...
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06/04/2022
First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spaces
From optimal transport to robust dimensionality reduction, a plethora of...
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05/15/2022
Online Nonsubmodular Minimization with Delayed Costs: From Full Information to Bandit Feedback
Motivated by applications to online learning in sparse estimation and Ba...
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05/06/2022
Perseus: A Simple High-Order Regularization Method for Variational Inequalities
This paper settles an open and challenging question pertaining to the de...
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04/07/2022
First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems
We consider the problem of computing an equilibrium in a class of nonlin...
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12/06/2021
Optimal No-Regret Learning in Strongly Monotone Games with Bandit Feedback
We consider online no-regret learning in unknown games with bandit feedb...
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11/15/2021
On Monotone Inclusions, Acceleration and Closed-Loop Control
We propose and analyze a new dynamical system with a closed-loop control...
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04/27/2021
Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization
Distributionally robust supervised learning (DRSL) is emerging as a key ...
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03/24/2021
A Variational Inequality Approach to Bayesian Regression Games
Bayesian regression games are a special class of two-player general-sum ...
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06/22/2020
On Projection Robust Optimal Transport: Sample Complexity and Model Misspecification
Optimal transport (OT) distances are increasingly used as loss functions...
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06/12/2020
Projection Robust Wasserstein Distance and Riemannian Optimization
Projection robust Wasserstein (PRW) distance, or Wasserstein projection ...
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02/23/2020
Finite-Time Last-Iterate Convergence for Multi-Agent Learning in Games
We consider multi-agent learning via online gradient descent (OGD) in a ...
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02/12/2020
Revisiting Fixed Support Wasserstein Barycenter: Computational Hardness and Efficient Algorithms
We study the fixed-support Wasserstein barycenter problem (FS-WBP), whic...
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02/12/2020
Fixed-Support Wasserstein Barycenters: Computational Hardness and Fast Algorithm
We study the fixed-support Wasserstein barycenter problem (FS-WBP), whic...
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02/12/2020
Computational Hardness and Fast Algorithm for Fixed-Support Wasserstein Barycenter
We study in this paper the fixed-support Wasserstein barycenter problem ...
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02/05/2020
Near-Optimal Algorithms for Minimax Optimization
This paper resolves a longstanding open question pertaining to the desig...
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12/16/2019
A Control-Theoretic Perspective on Optimal High-Order Optimization
In this paper, we provide a control-theoretic perspective on optimal ten...
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09/30/2019
On the Complexity of Approximating Multimarginal Optimal Transport
We study the complexity of approximating the multimarginal optimal trans...
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06/02/2019
On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems
We consider nonconvex-concave minimax problems, _x_y∈Y f(x, y), where f ...
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06/01/2019
On the Acceleration of the Sinkhorn and Greenkhorn Algorithms for Optimal Transport
We propose and analyze a novel approach to accelerate the Sinkhorn and G...
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04/16/2019
Global Error Bounds and Linear Convergence for Gradient-Based Algorithms for Trend Filtering and ℓ_1-Convex Clustering
We propose a class of first-order gradient-type optimization algorithms ...
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04/16/2019
On Structured Filtering-Clustering: Global Error Bound and Optimal First-Order Algorithms
In recent years, the filtering-clustering problems have been a central t...
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01/19/2019
On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms
We provide theoretical analyses for two algorithms that solve the regula...
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10/22/2018
Sparsemax and Relaxed Wasserstein for Topic Sparsity
Topic sparsity refers to the observation that individual documents usual...
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02/07/2018
Improved Oracle Complexity of Variance Reduced Methods for Nonsmooth Convex Stochastic Composition Optimization
We consider the nonsmooth convex composition optimization problem where ...
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02/07/2018
Improved Incremental First-Order Oracle Complexity of Variance Reduced Methods for Nonsmooth Convex Stochastic Composition Optimization
We consider the nonsmooth convex composition optimization problem where ...
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01/30/2018
An Incremental Path-Following Splitting Method for Linearly Constrained Nonconvex Nonsmooth Programs
The linearly constrained nonconvex nonsmooth program has drawn much atte...
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01/22/2018
On the Iteration Complexity Analysis of Stochastic Primal-Dual Hybrid Gradient Approach with High Probability
In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG...
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08/20/2017
Stochastic Primal-Dual Proximal ExtraGradient Descent for Compositely Regularized Optimization
We consider a wide range of regularized stochastic minimization problems...
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05/19/2017
Relaxed Wasserstein with Applications to GANs
We propose a novel class of statistical divergences called Relaxed Wasse...
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05/09/2016
Structured Nonconvex and Nonsmooth Optimization: Algorithms and Iteration Complexity Analysis
Nonconvex and nonsmooth optimization problems are frequently encountered...
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05/16/2015
Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems
The alternating direction method of multipliers (ADMM) has been successf...
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01/27/2013