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. 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 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.
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.
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. We study convergence rates of variational posterior distributions for nonparametric and high-dimensional inference. We formulate general conditions on prior, likelihood, and variational class that characterize the convergence rates. Under similar "prior mass and testing" conditions considered in the literature, the rat…
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.
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.
SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate as FGD (Full Gradient Descent) because of the inherent gradient variance. To attack the problem, mini-batch SGD was proposed to get a trade-o…
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.
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.
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.
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.
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. 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.
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.
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.
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.
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.
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. We estimate from above the rate at which a solution to the normalized Ricci flow on a closed manifold may converge to a limit soliton. Our main result implies that any solution which converges modulo diffeomorphisms to a soliton faster than any fixed exponential rate must itself be self-similar.
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.
Paper analyzes TD( λ λ λ ) convergence rates for arbitrary features.
problem Convergence rates for linear TD( λ λ λ ) under arbitrary features. method Developed a novel stochastic approximation result for arbitrary features.
result Established L 2 L^2 L 2 convergence rates for linear TD( λ λ λ ) without linearly independent features assumption. The article calculates the F \mathbb{F} F -convergence rate for Ricci flows with closed and smooth tangent flows.
problem Analyzing the convergence rate of Ricci flows with specific tangent flows.
method Calculating the F \mathbb{F} F -convergence rate for Ricci flows with closed and smooth tangent flows. result A Ricci flow with closed and smooth tangent flow is ∣ log λ ∣ − θ |\log λ|^{-θ} ∣ log λ ∣ − θ close to its tangent flow in the F \mathbb{F} F -sense. Study on interest rate model with jumps, proving strong convergence in simulations.
problem Analytical solutions for complex interest rate models with jumps are difficult.
method Employed truncated Euler-Maruyama techniques to prove strong convergence.
result Justified strong convergence for Monte Carlo calibration and valuation.
Bayesian method with Gaussian process priors achieves optimal convergence rates for regression function and its derivatives.
problem Estimating the regression function and its derivatives in nonparametric regression.
method Bayesian approach with Gaussian process priors, focusing on convergence rates and plug-in property.
result Equivalence of convergence rates of posterior distributions and Bayes estimators for regression function and its derivatives.
Study proves convergence of interest rate model approximations.
problem Investigating convergence of stochastic interest rate models.
method Developed analytical tools for true and truncated EM solutions, proving convergence in probability.
result True solution converges in probability to truncated EM solution as step size approaches zero.
Active data collection improves convergence rates in operator learning.
problem Improving convergence rates in operator learning with linear target and stochastic input.
method Active data collection strategies with mean-zero stochastic process and continuous covariance kernels.
result Achieves arbitrarily fast error convergence rates with eigenvalue decay of covariance kernels.
New theorem for generalized group sparsity improves consistency and convergence rates.
problem Improving statistical inference in high-dimensional data with element-wise and group-wise sparsity.
method Developed a generalized version of Sparse-Group Lasso and proved a universal theorem for consistency and convergence rates.
result Obtained results on consistency and convergence rates for different forms of double sparsity regularization.
This work analyzes the convergence rate of unrolling for optimizing quadratic objectives.
problem The challenge of accurately computing Jacobians through optimization.
method Non-asymptotic convergence-rate analysis of unrolled differentiation for gradient descent and Chebyshev method.
result There is a trade-off between fast asymptotic convergence and immediate but slower convergence due to the learning rate.
New loss function improves convergence rate for neural networks.
problem Improving convergence speed of neural networks for classification tasks.
method Proposes a modified hinge loss function with gradients to critical points.
result Margin converges to max-margin at O ( 1 / t ) \mathcal{O}(1/t) O ( 1/ t ) rate, faster than exponential losses. Step decay schedules improve convergence in non-convex optimization.
problem Improving convergence in non-convex optimization problems.
method Analyzing convergence rates of step decay schedules in non-convex, convex, and strongly convex problems.
result Step decay schedules achieve O ( ln T / T ) \mathcal{O}(\ln T/\sqrt{T}) O ( ln T / T ) convergence rates in various optimization scenarios. Convolutional neural networks improve image classification accuracy.
problem Improving accuracy in image classification.
method Analyzing the convergence rate of misclassification risk for image classifiers.
result A rate of convergence independent of image dimension proves the effectiveness of CNNs.
Study improves convergence rates for GVI under prior misspecification.
problem Improving convergence rates for GVI under prior misspecification.
method Proves rates of convergence and robustness to prior misspecification in GVI framework.
result Establishes sufficient conditions for existence and uniqueness of GVI posteriors.
Paper proposes a quasi-Newton method for nonlinear equations with global convergence guarantees.
problem Solving smooth and monotone nonlinear equations efficiently and globally.
method Hybrid proximal extragradient framework combined with online learning for Jacobian approximation.
result First global convergence results showing quasi-Newton method's advantage over extragradient method.