Convergence Analysis

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4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

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Near-Linear Accuracy Bounds for Moreau--Yosida Unadjusted Langevin Sampling
Sep 30, 2026Yuchen Xin, Zhihua ZhangMarkov Chain Monte Carlo Langevin Dynamics
School of Mathematical Sciences, Peking University
Adam under Generalized Smoothness with Second-Moment-Type Stochastic Gradients
Sep 29, 2026Ruinan Jin, Difei Cheng, Ling Chen +3Convergence Analysis Stochastic Optimization Convergence
Mohamed bin Zayed University of Artificial Intelligence · Aerospace Information Technology University · The Ohio State University +2
Convergent Plug-and-Play Image Restoration with Annealed Noise Levels
Sep 26, 2026Samuel HuraultConvergence Analysis Image Restoration
LIGM, CNRS, Univ. Gustave Eiffel
The Exact Time-Uniform Rate Frontier for Stochastic Gradient Descent on Smooth Convex Objectives
Sep 8, 2026Ruijie Li, Kang Chen, Tianyu WangLearning Rate Scheduling Last-Iterate Convergence
School of Data Science, Fudan University · Shanghai Center for Mathematical Sciences, Fudan University
Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling
Aug 13, 2026Yuchen Xin, Zhihua ZhangLangevin Dynamics Sample Complexity
School of Mathematical Sciences, Peking University
A Direct Route to Markov Chain Convergence via Asymptotic Equivalence with the Target
Aug 4, 2026Patrick ForréMarkov Chain Monte Carlo Convergence Analysis
AI4Science Lab Korteweg-de Vries Institute for Mathematics University of Amsterdam
Contraction Analysis of Holomorphic Dynamical Systems via the Intrinsic Kobayashi Metric
Aug 1, 2026Soumic SarkarDynamical Systems Convergence Analysis
Narva College, University of Tartu, Raekoja plats 2-319, Narva, 20307, Estonia
Learning Asymptotics with Convergence-Rate Guarantees using Linear Least Squares
Jul 25, 2026Christos N. EfremConvergence Analysis
Per-Token Fixed-Point Convergence in Depth-Recurrent Transformers
Jul 15, 2026Joe LoganTransformer Inference Recurrent Transformers
Independent researcher
Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling
Jul 6, 2026Stanislas Strasman, Gabriel Victorino Cardoso, Sylvain Le Corff +2Markov Chain Monte Carlo Markov Models
SU, LPSM · Sorbonne Université and Université Paris Cité, CNRS, LPSM, F-75005 Paris, France · LPSM +2
Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks
Jul 5, 2026Shokhrukh Ibragimov, Arnulf JentzenDeep Learning Optimization Neural Network Optimization
Applied Mathematics: Institute for Analysis and Numerics, University of Münster, Germany · School of Data Science and School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen), China
New Bounds for the Last Iterate of the Stochastic subGradient Method
Jun 23, 2026Guglielmo Beretta, Tommaso Cesari, Roberto Colomboni +1Stochastic Optimization Last-Iterate Convergence
Department of Computer Science, Aarhus University, Aarhus, Denmark · School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada · School of Mathematics, University of Bristol, Bristol, United Kingdom
GARIP: A Running-Average Moving Reference for Last-Iterate Self-Play in Two-Player Zero-Sum Games
Jun 21, 2026Can SavcıNash Equilibrium Last-Iterate Convergence
Independent Researcher İzmir, Türkiye
Last-Iterate Convergence of Optimistic Multiplicative Weight Update
Jun 10, 2026Francesco OrabonaLast-Iterate Convergence Optimization Convergence Analysis
King Abdullah University of Science and Technology (KAUST) Thuwal, 23955-6900, Kingdom of Saudi Arabia
Non-Vacuous Certification of Transport MCMC via Oscillation-Controlled Normalizing Flows
May 31, 2026Jun HuMarkov Chain Monte Carlo Normalizing Flows
China Sanya Science and Education Innovation Park, Wuhan University of Technology, Sanya 572025, China · School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China
Improved Guarantees for Langevin Monte Carlo with Average Smoothness
May 29, 2026Arnak S. Dalalyan, Avetik KaragulyanMarkov Chain Monte Carlo Stochastic Gradient Langevin Dynamics
CREST, ENSAE Paris, Institut Polytechnique de Paris and MBZUAI · L2S, CNRS, Centrale Supélec, Université Paris-Saclay
Non-Asymptotic Convergence of Stochastic Iterative Algorithms: A Lyapunov Framework
May 29, 2026Zaiwei Chen, Siva Theja MaguluriLyapunov Stability Stochastic Approximation
Purdue IE · Georgia Tech IE
Local linear convergence of gradient methods for overparameterized Gaussian mixtures
May 29, 2026Jingxing Wang, Vasileios Charisopoulos, Maryam FazelGradient Descent Gaussian Mixture Models
Electrical & Computer Engineering, University of Washington, Seattle, WA · National Institute for Theory and Mathematics in Biology, Chicago, IL · Amazon, Inc.
Self-Certifying Transport MCMC via Dual Spectral-Gap Certificates
May 29, 2026Jun HuMarkov Chain Monte Carlo Convergence Analysis
Wuhan University of Technology, Wuhan, China
Stability and Discretization Error of State Space Model Neural Operators
May 17, 2026Abderrahim Bendahi, Adrien Fradin, Johan Peralez +2Fourier Neural Operator Convergence Analysis
École polytechnique Paris, France · Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007 Villeurbanne, France · CNRS, UniversitéJulieLyonDigne1, INSA Lyon, LIRIS Lyon, France +1
Sign-Separated Asymmetric Finite-Time Error Analysis of Q-Learning
May 15, 2026Donghwan LeeQ-Learning Convergence Analysis
Department of Electrical Engineering Korea Advanced Institute of Science and Technology (KAIST) Daejeon 34141, South Korea
When and Why is Optimistic Multiplicative Weights Slow? The Geometry of Energy Dissipation
May 13, 2026John Lazarsfeld, Anas Barakat, Georgios Piliouras +2Nash Equilibrium Last-Iterate Convergence
SUTD · Google DeepMind · NUS CQT +2
Augmented Lagrangian Method for Last-Iterate Convergence for Constrained MDPs
May 12, 2026Michael Lu, Max Qiushi Lin, Mo Chen +1Markov Decision Processes Last-Iterate Convergence
Simon Fraser University
On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise
May 10, 2026Johannes Teutsch, Oleksii Molodchyk, Marion Leibold +2Kernel Regression Uncertainty Quantification
Chair of Automatic Control Engineering, Department of Computer Engineering, Technical University of Munich, 80333 Munich, Germany · Institute of Control Systems, Hamburg University of Technology, 21073 Hamburg, Germany · Department of Electrical and Computer Engineering, National University of Singapore, 117583 Singapore
Near-Optimal Last-Iterate Convergence for Zero-Sum Games with Bandit Feedback and Opponent Actions
May 10, 2026Soumita Hait, Ping Li, Haipeng Luo +1Last-Iterate Convergence Imperfect-Information Games
University of Southern California · Shanghai University of Finance and Economics · University of Iowa
Almost Sure Convergence Rates of Stochastic Approximation and Reinforcement Learning via a Poisson-Moreau Drift
May 8, 2026Xinyu Liu, Zixuan Xie, Shangtong ZhangReinforcement Learning Stochastic Approximation
University of Virginia
High-Probability Convergence in Decentralized Stochastic Optimization with Gradient Tracking
Apr 30, 2026Aleksandar Armacki, Haoyuan Cai, Ali H. SayedConvergence Analysis Stochastic Optimization Convergence
Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Identifiability and Stability of Generative Drifting with Companion-Elliptic Kernel Families
Apr 27, 2026HakGeun Lee, Hyonho ChunGenerative Modeling Convergence Analysis
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea.
The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback
Apr 17, 2026Côme Fiegel, Pierre Ménard, Tadashi Kozuno +2Nash Equilibrium Last-Iterate Convergence
ENSAE Paris - CREST, Palaiseau, France · Inria - FairPlay · ENS Lyon, Lyon, France +3
Optimal last-iterate convergence in matrix games with bandit feedback using the log-barrier
Apr 16, 2026Come Fiegel, Pierre Menard, Tadashi Kozuno +2Last-Iterate Convergence Imperfect-Information Games
ENSAE Paris – CREST, France · ENS Lyon, France · Isara Labs +2

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Near-Linear Accuracy Bounds for Moreau--Yosida Unadjusted Langevin Sampling

Yuchen Xin, Zhihua Zhang

School of Mathematical Sciences, Peking University

Markov Chain Monte Carlo Langevin Dynamics Log-Concave Sampling Convergence Analysis

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We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is

π\propto e^{-f-g}

, where

f\in C^2(\mathbb{R}^d)

m

-strongly convex with Lipschitz gradient and

g

is convex and globally Lipschitz. Under an explicit parameter-dependent step-size condition, we bound the invariant-measure bias relative to the Moreau-smoothed target by

\widetilde O(h)

, with only logarithmic dependence on the inverse smoothing parameter in the error coefficient. Combining this estimate with the Moreau approximation bias and Wasserstein contraction gives

\widetilde O(\varepsilon^{-1})

iterations to make the

N

th-iterate law

μ_N

satisfy

\sqrt m\,W_2(μ_N,π)\le\varepsilon

, for fixed model parameters and initialization. We bound the stationary error directly, without assuming third derivatives or a Lipschitz Hessian. Each iteration uses one gradient evaluation and one exact proximal evaluation. The key idea in our analysis is to convert a second-order stationary residual into a Wasserstein bound using a Poisson-based estimate.

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