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.
Algorithm learns smooth probability functions from Bernoulli tests with guarantees.
problem Learning smooth probability functions from Bernoulli tests with contextual features.
method Scalable algorithm with rigorous L2-norm convergence guarantees for posterior update rule.
result Empirical convergence rates match theoretical guarantees, superior to state-of-the-art.
This paper analyzes momentum Q-learning with finite-sample guarantees.
problem Improving Q-learning performance with momentum schemes.
method Proposes MomentumQ algorithm integrating Nesterov and Polyak's momentum schemes, analyzes convergence for function approximations.
result Establishes finite-sample convergence rates for MomentumQ, demonstrating better performance than vanilla Q-learning.
New algorithm improves convergence rates for convex optimization problems.
problem Convex optimization problems with noisy stochastic data.
method Stochastic proximal point algorithm with weak linear regularity condition.
result Achieves $\mathcal{O}\left(\frac{1}{k}
ight)$ convergence rate for SPP.
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
Paper derives convergence rates and confidence intervals for LSA with Markovian noise.
problem Analyzing convergence rates and constructing confidence intervals for LSA with Markovian noise.
method Derives non-asymptotic Berry-Esseen bounds and multiplier block bootstrap procedure.
result Provides O ( n − 1 / 4 ) \mathcal{O}(n^{-1/4}) O ( n − 1/4 ) convergence rates and guarantees consistent inference. The study provides statistical guarantees for Bayesian variational boosting.
problem Statistical and convergence issues in variational boosting.
method Proposed a novel variational family and a functional Frank-Wolfe optimization algorithm.
result Demonstrated stochastic boundedness and provided convergence rate for boosting iterates.
New method speeds up Gibbs sampling for large graphs.
problem Efficiently sampling from large graphical models.
method Poisson-minibatching Gibbs sampling.
result Theoretical convergence rate guarantees for Poisson-minibatching Gibbs.
New adaptive SGD algorithms for federated learning over physical channels.
problem Reducing communication cost in federated learning over physical channels.
method Proposed adaptive federated SGD algorithms considering channel noise and hardware constraints.
result Demonstrated convergence rates adaptive to stochastic gradient noise level.
Study guarantees convergence of mean shift mode estimation.
problem Ensuring reliable mode estimation in KDE using mean shift.
method Utilizes Łojasiewicz inequality to prove convergence rate.
result Extends convergence guarantees to biweight kernel.
Unified approach to compute asymptotic constants using optimization.
problem Computing unknown constants in asymptotic expansions.
method Linear Least Squares and Tikhonov Linear Least Squares methods.
result Rigorous asymptotic estimates and convergence-rate guarantees.
New method improves sampling efficiency for complex distributions.
problem Sampling from distributions with high condition numbers and constraints.
method Riemannian Hamiltonian Monte Carlo with numerical integrators.
result Convergence rate is independent of condition number and polytope geometry.
Guarantees convergence for black-box variational inference without modifications.
problem Convergence guarantees for black-box variational inference.
method Analysis of log-smooth posterior densities, location-scale variational family, and convergence rates of algorithm design choices.
result Proximal stochastic gradient descent fixes suboptimal convergence rates and achieves strongest known guarantees.
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.
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.
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.
We introduce a new concept, data irrecoverability, and show that the well-studied concept of data privacy is sufficient but not necessary for data irrecoverability. We show that there are several regularized loss minimization problems that can use perturbed data with theoretical guarantees of generalization, i.e., loss…
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. 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 convergence rates for shuffling gradient methods without strong convexity.
problem Theoretical gap between shuffling gradient methods' empirical success and established convergence rates.
method Proved last-iterate convergence rates for shuffling gradient methods using function value gap.
result First last-iterate convergence rates for shuffling gradient methods without strong convexity.
This paper advances extragradient methods for solving inclusions under co-hypomonotonicity.
problem Solving inclusions with non-Lipschitz mappings.
method Unified and generalized extragradient methods under co-hypomonotonicity.
result Achieved O ( 1 / k ) \mathcal{O}(1/k) O ( 1/ k ) convergence rates for residual norms. Cubic-regularized Newton's method (CR) is a popular algorithm that guarantees to produce a second-order stationary solution for solving nonconvex optimization problems. However, existing understandings of the convergence rate of CR are conditioned on special types of geometrical properties of the objective function. In…
New algorithm protects privacy in IVaR regression while maintaining accuracy.
problem Privacy leakage in classical IVaR methods.
method Noisy two-stage gradient descent with differential privacy guarantees.
result Achieves statistical efficiency and privacy in IVaR regression.
Improved analysis of accelerated noisy power method for PCA.
problem Inexact matrix-vector products in PCA settings.
method Improved analysis of Accelerated Noisy Power Method under milder perturbation conditions.
result Worst-case optimal convergence rate with relaxed noise conditions.
New method improves convergence rates for stochastic convex optimization.
problem Convergence guarantees for online learning algorithms.
method Black-box modification to online learning algorithms, combined with optimistic and adaptive techniques.
result Achieves optimal accelerated rates of O ( L / T 2 + σ / T ) O(L/T^2 + σ/\sqrt{T}) O ( L / T 2 + σ / T ) . New algorithm optimizes convex functions with noisy evaluations in one dimension.
problem Optimizing convex functions with noisy zero-order evaluations in one dimension.
method Proposed a computationally efficient algorithm achieving O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) convergence rate. result Achieved the optimal O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) convergence rate, closing the gap in one dimension. The paper provides theoretical guarantees for neural network-based anomaly detection.
problem Theoretical guarantees for unsupervised neural network-based anomaly detection.
method Casting anomaly detection as a binary classification problem, establishing non-asymptotic upper bounds and convergence rates.
result The convergence rate on the excess risk matches the minimax optimal rate.
A new cost-frugal HPO method controls training cost during optimization.
problem Ignoring training cost variation in HPO leads to inefficient hyperparameter tuning.
method Developed a randomized direct-search method with convergence and approximation guarantees.
result Proved an O ( d K ) O(\frac{\sqrt{d}}{\sqrt{K}}) O ( K d ) convergence rate and O ( d ε − 2 ) O(dε^{-2}) O ( d ε − 2 ) approximation guarantee. 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.
New shuffling methods improve convergence without Lipschitz smoothness.
problem Lack of convergence guarantees for shuffling methods under non-Lipschitz conditions.
method Revisit shuffling methods, prove convergence under general bounded variance condition.
result Matched current best-known convergence rates without Lipschitz smoothness.
New analysis proves consistency for adaptive Bayesian quadrature methods.
problem No theoretical guarantees for adaptive Bayesian quadrature methods.
method Introduces weak adaptivity and proves consistency for a broad class of adaptive Bayesian quadrature rules.
result Proves consistency and derives non-tight but informative convergence rates for adaptive Bayesian quadrature methods.
New algorithm reduces privacy loss in SGD without learning rate tuning.
problem Locally differentially private stochastic optimization with high privacy loss.
method BANCO (Betting Algorithm for Noisy COins) for ε ε ε -LDP SGD. result Matches convergence rate of tuned SGD without learning rate tuning.
New convergence rates found for PnP methods using MMSE denoisers.
problem Asymptotic convergence of PnP methods with MMSE denoisers.
method Explicitly represented MMSE denoiser as an upper Moreau envelope, derived sublinear convergence rates.
result First sublinear convergence guarantee for PnP proximal gradient descent with MMSE denoiser.
The paper analyzes the convergence rates of smooth message passing algorithms in entropy-regularized MAP inference.
problem Finding the most likely configuration in graphical models with combinatorial optimization.
method Entropy-regularized linear programming relaxations and smooth message passing algorithms.
result The number of iterations sufficient to recover the true integral MAP solution is determined.
A new hybrid-ordered SGD method reduces communication and complexity for non-convex optimization.
problem Balancing communication, computational complexity, and convergence rate in distributed non-convex optimization.
method Hybrid-ordered distributed SGD with pre-shared scalers and periodic vector communication.
result Order-wise faster convergence compared to existing methods.
Bayesian neural network achieves nearly optimal performance in Besov space.
problem Bayesian neural networks in Besov space.
method Spike-and-slab prior and shrinkage prior for posterior convergence rate.
result The posterior convergence rate is nearly minimax and adaptive to unknown smoothness.
Paper proposes a new method to optimize deep neural networks with sparse regularization.
problem Difficulty in achieving optimal convergence rates for deep neural networks due to sparsity constraints.
method Introduces a novel penalized estimation method for sparse DNNs, resolving computational and theoretical issues.
result Establishes an oracle inequality for the excess risk of the proposed sparse-penalized DNN estimator and derives convergence rates.
DDPMs are robust to noisy score estimates and achieve optimal convergence rates in Wasserstein-2 distance.
problem Evaluating the quality of DDPMs in Wasserstein distance with noisy score estimates.
method Established finite-sample guarantees in Wasserstein-2 distance for DDPMs, considering noisy score estimates.
result Optimal convergence rates in Wasserstein-2 distance for DDPMs, matching Gaussian case.
We study the convergence rate of stochastic optimization of exact (NP-hard) objectives, for which only biased estimates of the gradient are available. We motivate this problem in the context of learning the structure and parameters of Ising models. We first provide a convergence-rate analysis of deterministic errors fo…
Paper improves convergence rates and step sizes for gradient algorithms.
problem Limited convergence rates and step sizes in existing algorithms.
method General proximal incremental aggregated gradient algorithm.
result Better and novel convergence results under general scheme.
The paper analyzes convergence rates of bilevel optimization algorithms and introduces a new stochastic algorithm.
problem Nonconvex-strongly-convex bilevel optimization problems in machine learning.
method Comprehensive convergence rate analysis for deterministic bilevel optimization using AID and ITD, and a novel stochastic algorithm stocBiO.
result Theoretical convergence rates for AID and ITD methods, and stocBiO's superior performance.
RSGDA improves convergence rates for nonconvex-strongly concave optimization.
problem Optimization of nonconvex-strongly concave problems.
method Randomized Stochastic Gradient Descent Ascent (RSGDA) with optimal loop sizes.
result First almost sure convergence rates for SGDA algorithms on nonconvex-strongly concave settings.
Paper analyzes convergence of FedAvg on non-iid data and provides theoretical guarantees.
problem Analyzing convergence of Federated Averaging on non-iid data.
method Theoretical analysis of convergence rate and trade-offs between communication-efficiency and convergence rate.
result Established a convergence rate of O ( 1 T ) \mathcal{O}(\frac{1}{T}) O ( T 1 ) for strongly convex and smooth problems. Paper extends MLFD to signed measures via bilevel approach.
problem Risk minimization for infinite width neural networks and sparse deconvolution.
method Bilevel reduction to extend MLFD to signed measures, investigating convergence rates.
result Improved convergence rates for bilevel MFLD in low-noise regime and local exponential convergence for single neuron learning.
The paper applies momentum to CR Newton's method for nonconvex optimization, improving convergence.
problem Improving convergence in nonconvex optimization problems.
method Applying momentum to cubic regularized Newton's method.
result CR with momentum achieves the best convergence rate to second-order stationary points.
The paper analyzes GNNs with one hidden layer, proving their generalizability and convergence rate.
problem Theoretical guarantee on generalizability of GNNs with one hidden layer.
method Tensor initialization and accelerated gradient descent.
result The proposed learning algorithm converges to the ground-truth GNN model for regression and to a model close to the ground-truth for binary classification.
New algorithms prove fast convergence in complex min-max problems.
problem Proving fast convergence in nonconvex min-max optimization.
method Hamiltonian Gradient Descent (HGD) and Consensus Optimization (CO) algorithms.
result HGD and CO achieve linear convergence in various settings.
This work accelerates gradient descent with anytime convergence guarantees.
problem Improving the convergence rate of gradient descent methods.
method Proposes a stepsize schedule for gradient descent that achieves anytime convergence rates.
result Gradient descent can achieve convergence rates of O ( T − 1.119 ) O(T^{-1.119}) O ( T − 1.119 ) for any stopping time T T T .