Study on convergence rate of Q Q Q -curvature flow in 6 dimensions.
problem Analyzing the convergence rate of Q Q Q -curvature flow in 6 dimensions. method Provided an example of a slowly converging Q 6 Q_6 Q 6 -curvature flow in dimension 6. result The Q Q Q -curvature flow in 6 dimensions does not always converge exponentially, unlike in 2 dimensions. Estimates the maximal rate of convergence for Ricci flow solutions.
problem Understanding the maximal rate of convergence of Ricci flow solutions.
method Estimates the rate from above for solutions converging to solitons.
result Solutions converging faster than any fixed exponential rate must be self-similar.
Study on the convergence rate of prescribed scalar curvature flow.
problem Prescribing scalar curvature on manifolds.
method Inspired by Yamabe flow convergence rate study, analyze the prescribed scalar curvature flow convergence rate.
result Determine the convergence rate of the prescribed scalar curvature flow.
Study on convergence rate of weighted Yamabe flow.
problem Weighted Yamabe problem on smooth metric measure spaces.
method Weighted Yamabe flow and its convergence rate analysis.
result Study and analysis of convergence rate of the weighted Yamabe flow.
Study convergence rates of variational posterior distributions for inference.
problem Characterize convergence rates of variational posterior distributions for nonparametric and high-dimensional inference.
method Formulate general conditions on prior, likelihood, and variational class to characterize convergence rates. Propose novel prior mass conditions for specific prior distributions.
result The convergence rate of variational posterior distributions is the sum of the convergence rate of the true posterior and the variational approximation error.
Study shows convergence rates for BSDEs approximated by compound Poisson processes.
problem Analyzing convergence rates of BSDEs driven by Lévy processes.
method Approximating Lévy processes by compound Poisson processes and studying BSDEs.
result Optimal convergence rates derived for BSDEs in L 2 \mathbb L^2 L 2 -norm and Wasserstein distance. Estimates the rate of convergence of mean curvature flow solutions.
problem Understanding the convergence rate of mean curvature flow solutions.
method Estimates the upper bound of convergence rate to a limit self-similar solution.
result Solutions converging faster than any fixed exponential rate must be shrinkers themselves.
New metric for G2 manifold with slow convergence rate near singularity.
problem Understanding the convergence rate near isolated singularities in G2 manifolds.
method Constructed a metric with G2 holonomy on a ball inside the cone over the flag manifold.
result Demonstrated a metric with a slow rate of convergence to the cone metric near the singularity.
Paper establishes convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
problem Analyzing convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
method Novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing length.
result First almost sure convergence rate and maximal concentration bound with exponential tails for contractive stochastic approximation algorithms with Markovian noise.
Optimal bounds proven for ordinal embedding convergence rate.
problem Optimal bounds for ordinal embedding convergence rate in 1D.
method Utilized results from additive number theory and conducted computational experiments.
result Proved optimal bounds for convergence rate in 1D.
Study on convergence rate of Bergman metrics on Kähler manifolds.
problem Analyzing convergence rate of Bergman metrics on Kähler manifolds.
method Using Tian's peak section method to show uniform C 1 , α C^{1,α} C 1 , α convergence. result Uniform C 1 , α C^{1,α} C 1 , α convergence of Bergman metrics is demonstrated. Improved SGD methods converge faster for nonconvex optimization.
problem Nonconvex optimization challenges in machine learning.
method Adaptive SGD with line-search and Polyak stepsizes.
result Unified convergence rates for various nonconvex functions.
The paper studies convergence rates of Tsallis entropic regularization in optimal transport.
problem Optimal transport with regularization.
method Γ-convergence and quantization/shadow arguments.
result Derives convergence rate of Tsallis entropic regularization.
Paper analyzes faster convergence rates for reinforcement learning from offline data.
problem Analyzing faster convergence rates for reinforcement learning from offline data.
method Fine analysis of reinforcement learning from offline data, providing fast rates for regret convergence.
result The paper provides fast rates for the regret convergence, showing that the level of exponentiation depends on the noise in the decision-making problem.
Study shows LDA topic models converge at rate n^-1/4 without strict topic separability.
problem Convergence rates of Latent Dirichlet Allocation (LDA) topic models.
method Maximum likelihood estimator, Wasserstein's distance metric, without separability or non-degeneracy assumptions.
result Maximum likelihood estimator converges at rate n^-1/4, optimal in worst case.
Paper proves convergence rates for Gaussian kernel ridge regression.
problem Understanding convergence rates for Gaussian kernel ridge regression.
method Establishes polynomial convergence rates for KRR with fixed hyperparameters.
result First polynomial convergence rates for Gaussian kernel ridge regression.
Exponential rate of convergence for harmonic heat flow maps.
problem Analyzing the convergence rate of harmonic heat flow maps.
method Proving exponential convergence rate for harmonic heat flow maps.
result Exponential convergence rate of the harmonic heat flow.
PAGE optimizes nonconvex problems with optimal convergence rates.
problem Nonconvex optimization problems.
method PAGE algorithm for achieving optimal convergence rates.
result PAGE achieves optimal convergence rates for nonconvex optimization.
Near-Exponential Convergence Rates for kNN Classification
problem Convergence rates for kNN classification
method Introducing Boltzmann margin
result First near-exponential convergence rates for kNN classification
Gradient descent achieves exact linear convergence rate for symmetric matrix completion.
problem Low-rank symmetric matrix completion using gradient descent.
method Local analysis of gradient descent for symmetric matrices without additional assumptions.
result Closed-form expression of exact linear convergence rate matches practice.
A new algorithm SSAG reduces gradient variance to achieve linear convergence in large-scale optimization.
problem Achieving linear convergence rate in large-scale optimization problems due to gradient variance.
method Introduces SSAG, a novel algorithm that combines stratified sampling and averaging over iterations to reduce gradient variance.
result SSAG achieves linear convergence rate of O((1-μ/(8CL))^k) with smaller storage and iterative costs, depending mainly on class variance.
Averaged SGD achieves optimal convergence rate for neural networks in the NTK regime.
problem Convergence analysis of averaged stochastic gradient descent for neural networks.
method Analyzed convergence of averaged stochastic gradient descent for overparameterized two-layer neural networks.
result Achieved minimax optimal convergence rate with global convergence guarantee.
Improved convergence rates for MLE in mixture models using penalized log-likelihood.
problem Convergence rates for MLE in finite mixture models.
method Penalizing log-likelihood to discourage vanishing mixing weights, using Wasserstein distance and new loss functions.
result Improved convergence rates for some mixture components, faster than traditional methods.
Simpler, parameter-free AdaGrad and Adam variants with convergence guarantees.
problem Inefficiencies in ad-hoc learning rate tuning for optimization algorithms.
method Developed AdaGrad++ and Adam++ without predefined learning rates and proved their convergence.
result AdaGrad++ and Adam++ achieve comparable convergence rates to AdaGrad and Adam respectively.
Super-convergence allows neural nets to train faster with large learning rates.
problem Training neural networks too slowly.
method Training with large learning rates and one learning rate cycle.
result Neural networks can be trained an order of magnitude faster.
SGD method converges to minima for non-convex functions.
problem Non-convex optimization problems in machine learning.
method Stochastic gradient descent method for non-convex objective functions.
result Estimates on the rate of convergence to minima.
Alternative proof for convergence rate of three operator splitting scheme.
problem Optimizing composite functions with specific operator properties.
method Three operator splitting scheme for optimizing composite functions.
result Sublinear rate of convergence proved for the method.
Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.
problem Set membership estimation for linear systems with disturbances bounded by convex sets.
method Adopted block-martingale small-ball condition and random perturbed control policies to establish convergence rates.
result Established convergence rates for disturbances bounded by general convex sets.
New factorial power constants improve optimization convergence rates.
problem Optimization convergence rates depend on various constants.
method Proposes using factorial powers for defining these constants.
result Factorial powers simplify or improve convergence rates of optimization methods.
Paper shows convergence rates for stochastic processes.
problem Analyzing convergence rates for stochastic processes.
method Quantitative convergence in W 2 W_2 W 2 for Langevin-like processes. result Iterates converge to an invariant distribution at rate O ( 1 / k ) O(1/\sqrt{k}) O ( 1/ k ) . Study provides convergence rates for risk measure estimation.
problem Estimating risk measures from limited data.
method Plug-in estimation using empirical measures.
result Non-asymptotic convergence rates for risk measure estimation.
The paper analyzes convergence rates for SGD and SHB methods.
problem Analyzing convergence rates for stochastic gradient descent and heavy ball methods.
method Stochastic gradient descent and stochastic heavy ball method for general stochastic approximation problems.
result The last iterate of SHB converges almost surely to a minimizer and has faster convergence rates than SGD.
Last iterate of Extragradient algorithm converges slower than averaged iterates in saddle point problems.
problem Smooth convex-concave saddle point problems
method Analysis of Extragradient (EG) algorithm convergence rates
result The last iterate of EG converges at a rate of O(1/√T), compared to O(1/T) for averaged iterates
Polynomial networks converge to Gaussian processes at a rate of O(n^(-1/2)).
problem Understanding the convergence rate of polynomial networks to Gaussian processes.
method Examined one-hidden-layer neural networks with random weights, focusing on polynomial activations and their convergence rate in the 2-Wasserstein metric.
result The rate of convergence for polynomial networks to Gaussian processes is $O(n^{- rac{1}{2}})$ .
Improves understanding of stochastic NGVI convergence rates.
problem Lack of knowledge about non-asymptotic convergence rates in stochastic NGVI.
method Proved non-asymptotic convergence rates for conjugate likelihoods and showed implicit optimization for non-conjugate likelihoods.
result First O ( 1 T ) \mathcal{O}(\frac{1}{T}) O ( T 1 ) non-asymptotic convergence rate for stochastic NGVI in conjugate likelihoods. Corrects mistakes in convergence rate claims for SGD learning rate scheme.
problem Incorrect convergence rate claims for SGD learning rate scheme.
method Revised the convergence rate claims based on corrected test criterion for a series.
result Valid convergence rate of SGD is O ( 1 / t ) \mathcal{O}(1/t) O ( 1/ t ) , not O ( 1 / t 2 ) \mathcal{O}(1/t^2) O ( 1/ t 2 ) as previously stated. Paper studies convergence rates from surrogate risk minimizers to Bayes optimal classifier.
problem Analyzing the convergence rates of surrogate risk minimizers to the Bayes optimal classifier.
method Introducing consistency intensity to characterize surrogate loss functions and using it to derive convergence rates.
result Empirical surrogate risk minimizers converge faster to the Bayes optimal classifier under certain conditions.
Semi-supervised EM improves convergence rate with labeled samples.
problem Improving convergence rate in EM algorithm with labeled and unlabeled data.
method Analysis of semi-supervised EM algorithm for Gaussian mixture models.
result Labeled samples significantly improve the convergence rate for the EM algorithm.
A new decentralized optimization method with independent step-sizes and separated convergence rates.
problem Decentralized optimization with composite objective terms.
method Proximal-gradient algorithm with uncoordinated step-sizes and separated convergence rates.
result Linear convergence for special case without non-smooth terms under strong convexity.
New method improves simulation efficiency in high dimensions.
problem Efficiency in estimating functionals of conditional expectations in high dimensions.
method Kernel ridge regression exploiting smoothness of conditional expectation.
result Effective reduction of the curse of dimensionality, bridging convergence rates.
The paper improves spectral convergence rates for graph Laplacians.
problem Improving spectral convergence rates for graph Laplacians.
method Utilizing regularity of continuum eigenfunctions and strong pointwise consistency results.
result Eigenvalues and eigenvectors of graph Laplacian converge to continuum at rate O ( n − 1 / ( m + 4 ) ) O(n^{-1/(m+4)}) O ( n − 1/ ( m + 4 ) ) . Sharp bounds on weak convergence rate for rough volatility models.
problem Understanding the convergence rate in discretizing rough volatility models.
method Analyzing general and linear models to derive bounds.
result Sharper bound of \(H + 1/2\) for linear models.
Study shows rate of convergence for particle approximation of PDEs in Wasserstein space.
problem Analyzing convergence rates for particle approximations of PDEs in Wasserstein space.
method Backward stochastic differential equations techniques.
result Proved a rate of convergence of order 1/N for pathwise error and 1/sqrt(N) for L2-error on the derivative.
Paper analyzes convergence rates for multi-agent learning in games.
problem Convergence rates for multi-agent learning in games.
method Characterizes finite-time convergence rates for joint OGD learning on λ λ λ -cocoercive games and develops adaptive algorithms. result Adaptive algorithms achieve same convergence rates as non-adaptive counterparts.
Kolmogorov-Arnold Networks achieve optimal convergence rates in nonparametric regression.
problem Nonparametric function approximation in multivariate settings.
method Structured additive and multiplicative KANs using B-splines.
result Achieve minimax-optimal convergence rate O ( n − 2 r / ( 2 r + 1 ) ) O(n^{-2r/(2r+1)}) O ( n − 2 r / ( 2 r + 1 ) ) for Sobolev space functions. Study on convergence rates for optimal transport with regularization.
problem Convergence analysis of divergence-regularized optimal transport.
method Novel methodology using quantization and martingale couplings.
result Sharp rates for various divergences and transport costs.
Paper shows SVM can achieve super fast convergence rates.
problem Understanding fast convergence rates for SVM.
method Presented a simple mechanism to obtain fast convergence rates for SVM.
result SVM can exhibit exponential convergence rates without hard Tsybakov margin condition.
The Sinkhorn-Knopp derivatives converge with linear rate.
problem Optimal transport problem with entropic regularization.
method Iterative proportional fitting procedure.
result Derivatives converge with linear rate.