Nesterov SGD doesn't accelerate over SGD in over-parameterized learning.
problem Theoretical and practical acceleration of SGD with momentum in over-parameterized learning.
method Introducing a compensation term to Nesterov SGD, resulting in MaSS algorithm.
result MaSS converges for same step sizes as SGD and achieves accelerated convergence rates over SGD.
Proof given for SGD convergence in a concise manner.
problem Convergence of Stochastic Gradient Descent (SGD)
method Self-contained proof
result SGD convergence proven
SGD with large learning rates can converge to local maxima.
problem Understanding the behavior of SGD with large learning rates.
method Constructing worst-case optimization problems.
result SGD can converge to local maxima under certain conditions.
Communication-efficient SGD algorithms, which allow nodes to perform local updates and periodically synchronize local models, are highly effective in improving the speed and scalability of distributed SGD. However, a rigorous convergence analysis and comparative study of different communication-reduction strategies rem…
Unified analysis of SGD and GD convergence rates.
problem Analyzing convergence rates of SGD and GD methods.
method Unified proof for convergence of SGD on μ-convex functions under mild smoothness assumptions.
result Convergence rates match best known iteration complexities up to constants.
RS-NSGD improves SGD convergence for heavy-tailed noise.
problem Nonconvex optimization with heavy-tailed noise.
method Integrates direction normalization into subspace updates.
result Achieves better oracle complexity than full-dimensional normalized SGD.
Theoretical justification for large batch SGD converging to flatter minima.
problem Understanding the convergence of large batch SGD to flatter minima.
method Theoretical analysis of SGD in finite-time and asymptotic regimes.
result SGD tends to converge to flatter minima regardless of batch size, but with different rates.
This paper improves Minibatch SGD convergence through typicality sampling.
problem Slow convergence of Minibatch SGD due to large gradient noise.
method Typicality sampling for more efficient batch selection.
result Typical batch SGD outperforms conventional Minibatch SGD in convergence.
In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors of VR-SGD are set to the average and last iterate of the previous epoch, respecti…
Study reveals convergence properties of SGD with random learning rate.
problem Analyzing convergence of SGD with random learning rate in non-convex optimization.
method Introduced Poisson SGD with random learning rate and used stationary distribution analysis.
result Poisson SGD converges to a stationary distribution and finds global minima in non-convex optimization.
SGD converges globally to logistic loss minima for two-layer nets.
problem Global convergence of SGD for logistic loss on two-layer neural nets.
method Demonstrates existence of Frobenius norm regularized logistic loss functions as Villani functions, proving convergence and exponential rate.
result SGD converges globally to the global minima of appropriately regularized logistic empirical risk of depth 2 nets.
LAGS-SGD optimizes deep learning training by sparsifying gradients layer-wise.
problem Reduces long training times in large deep neural networks with distributed S-SGD.
method Layer-wise adaptive gradient sparsification combined with S-SGD.
result LAGS-SGD achieves convergence guarantees and outperforms vanilla S-SGD.
This paper improves convergence guarantees for SGD algorithms in non-convex smooth functions.
problem Theoretical convergence properties of SGD algorithms for non-convex smooth functions.
method Analysis of SGD algorithms with arbitrary data ordering for non-convex smooth functions.
result Enhanced convergence guarantees for incremental gradient and single shuffle SGD, improving the optimization term of convergence guarantee.
Paper removes bounded gradient assumption for SGD in nonconvex learning.
problem Existing theoretical results for SGD in nonconvex learning require uniform boundedness of gradients, which is hard to verify.
method Establishes sufficient conditions for SGD convergence without bounded gradient assumption.
result SGD achieves optimal convergence rates for nonconvex and gradient-dominated objectives.
SGD converges to global minimum for certain non-convex functions.
problem Theoretical challenges in optimizing non-convex functions in machine learning.
method Perturbed SGD on a broad class of non-convex functions.
result SGD converges to global minimum for certain non-convex functions.
Studied SGD convergence under weak conditions.
problem Convergence of SGD in nonconvex optimization.
method Analyzed biased nonconvex SGD under mild conditions.
result Provided convergence rates and complexities.
SGD converges exponentially fast in non-convex over-parametrized learning.
problem Convergence of SGD in non-convex, over-parametrized learning.
method Analysis of SGD with constant step size for non-convex functions satisfying the PL condition.
result Exponential convergence of SGD for non-convex functions satisfying the PL condition.
Improved Local SGD convergence for general convex objectives with bounded second-order heterogeneity.
problem Understanding when and why Local SGD outperforms alternatives in distributed optimization.
method Established improved convergence guarantees for Local SGD on general convex objectives under bounded second-order heterogeneity.
result Upper bounds for Local SGD are nearly tight, providing a sharper convergence theory.
SGD converges to global minimum in deep learning via star-convex path.
problem Understanding how SGD trains deep neural networks to global minimum.
method Exploiting star-convex path and zero loss value properties of SGD.
result SGD converges deterministically to global minimum in deep learning.
Global convergence of SGD proven for two-layer neural nets with regularization.
problem Proving global convergence of SGD for two-layer neural nets.
method Regularized empirical risk, SGD iterates, Villani functions.
result Global convergence of SGD for a special class of initializations.
SGD methods fail to converge to global minimizers in deep neural networks with ReLU activation.
problem Failure of SGD methods to converge to global minimizers in deep neural networks.
method Stochastic Gradient Descent (SGD) and its variants like Adam, RMSProp, etc.
result SGD methods fail to converge to global minimizers with high probability in deep neural networks with ReLU activation.
Paper introduces elastic consistency for distributed SGD, enabling convergence analysis.
problem Training large-scale machine learning models in distributed environments.
method Introduces elastic consistency as a general consistency model for distributed SGD.
result Derives convergence bounds for various distributed SGD methods.
Analysis of SGD+M convergence rates in high dimensions with batch size considerations.
problem Understanding convergence rates of SGD+M in high-dimensional settings.
method Analyzing the dynamics of SGD+M on least squares problems with large batch sizes and dimensions.
result Identifies the implicit conditioning ratio (ICR) that regulates SGD+M's acceleration and convergence rates.
This paper analyzes convergence of DP-SGD with adaptive quantile clipping.
problem Empirical success of adaptive clipping methods lacks theoretical understanding.
method Comprehensive convergence analysis of SGD with quantile clipping (QC-SGD).
result Establishes theoretical guarantees for DP-QC-SGD, revealing relationships between quantile selection, step size, and convergence.
The paper analyzes how hyperparameters affect SGD with momentum's convergence rate.
problem The role of hyperparameters in SGD with momentum's convergence rate.
method Theoretical analysis using a hyperparameters-dependent stochastic differential equation (hp-dependent SDE).
result The optimal linear rate of convergence depends on both the learning rate and the momentum coefficient.
DReg boosts large-batch SGD's generalization and convergence.
problem Large-batch SGD struggles with generalization in deep learning.
method DReg replicates a layer to encourage parameter diversity.
result DReg improves generalization and convergence with large-batch SGD.
Gradient clipping helps private SGD converge despite potential bias.
problem Gradient clipping in private SGD can bias convergence.
method Theoretical analysis and empirical evaluation of gradient clipping effects.
result Gradient clipping can prevent convergence to stationary points and introduces bias.
New convergence bounds for shuffling-based SGD methods in distributed learning.
problem Analyzing the performance of shuffling-based variants of SGD in distributed learning.
method Study of minibatch and local Random Reshuffling methods, proving convergence bounds and lower bounds.
result Shuffling-based variants converge faster than with-replacement sampling methods, and the bounds are tight.
Label noise in SGD helps converge to flatter minima.
problem Improving generalization in overparametrized models.
method Analyzes SGD with label noise, showing convergence to regularized minima.
result SGD with label noise converges to flatter minima, improving generalization.
SGD transitions between maxima and minima with varying time scales.
problem Understanding SGD's behavior near critical points in noisy landscapes.
method Analyzing SGD convergence and escape dynamics in 1D landscapes with infinite- and finite-variance noise.
result SGD reliably moves to the basin's minimum unless close to a local maximum, where it can linger.
Unified analysis for decentralized SGD across various topologies and updates.
problem Analysis of decentralized SGD methods with changing topologies and local updates.
method Unified convergence analysis covering local SGD updates and adaptive network topology.
result Universal convergence rates for smooth problems, interpolating between heterogeneous and iid-data settings.
SGD converges almost surely in non-convex problems, avoiding saddle points and accelerating convergence.
problem Understanding convergence of SGD in non-convex optimization problems.
method Analysis of SGD trajectories, focusing on boundedness, convergence to strict saddle points, and rate of convergence.
result SGD converges almost surely to a minimizer in non-convex problems, avoiding strict saddle points.
Sparsification improves convergence in asynchronous distributed SGD, even in the presence of staleness.
problem Staleness in asynchronous distributed SGD.
method Applied sparsification to reduce communication overheads in distributed asynchronous settings.
result The ergodic convergence rate of sparsified asynchronous SGD matches that of vanilla SGD, $\mathcal{O} \left( 1/\sqrt{T}
ight)$, even in the presence of staleness.
SGD converges with positive probability for non-convex deep neural networks under specific conditions.
problem Convergence of SGD for non-convex deep neural networks.
method Established local convergence with positive probability under local Łojasiewicz condition and additional structural assumption.
result SGD converges with positive probability for non-convex deep neural networks under specific conditions.
Proposes a new adaptive learning rate for SGD.
problem Finding an efficient learning rate for SGD.
method Stochastic Polyak step-size (SPS).
result SGD with SPS converges faster for over-parameterized models.
SQuARM-SGD improves decentralized SGD efficiency with momentum.
problem Efficient decentralized training of large-scale models over networks.
method Fixed local SGD steps with Nesterov's momentum, sparsified and quantized updates, locally computed triggering criterion.
result Convergence rate matches vanilla SGD, momentum improves test performance.
SGD converges to global minimum for structured non-convex functions.
problem Optimizing non-convex functions using SGD with slow convergence rates.
method Convergence theorems for SGD on structured non-convex functions, including Quasar and PL conditions.
result SGD converges to global minimum for specific non-convex functions under certain conditions.
Study on SGD for overparameterized neural networks, focusing on convergence rates.
problem Understanding convergence rates of SGD in overparameterized two-layer neural networks.
method Combines NTK approximation with RKHS analysis to explore SGD dynamics.
result Established sharp convergence rates for SGD in overparameterized two-layer neural networks.
Study uses SGD to learn operators in Hilbert spaces with convergence analysis.
problem Learning operators in general Hilbert spaces with SGD.
method Proposes weak and strong regularity conditions for convergence analysis.
result SGD converges to best linear approximation of nonlinear operators.
Paper analyzes D-SGD convergence with heterogeneous data and proposes topology learning.
problem Efficiently dealing with data heterogeneity in decentralized learning.
method Revisits D-SGD analysis, introduces neighborhood heterogeneity, and proposes topology learning.
result Formulates topology learning as a tractable optimization problem and demonstrates its effectiveness.
Most commonly used distributed machine learning systems are either synchronous or centralized asynchronous. Synchronous algorithms like AllReduce-SGD perform poorly in a heterogeneous environment, while asynchronous algorithms using a parameter server suffer from 1) communication bottleneck at parameter servers when wo…
Unified analysis of asynchronous-SGD algorithms for distributed learning.
problem Analyzing asynchronous-SGD in heterogeneous settings with varying speeds and data distributions.
method Unified convergence theory for non-convex smooth functions, including pure asynchronous SGD and its modifications.
result Unified convergence rates for various asynchronous algorithms, including novel methods.
Unified analysis of SGD variants for nonconvex federated optimization.
problem Performance of stochastic gradient methods in nonconvex optimization.
method Proposed a unified assumption for modeling stochastic gradient second moment, leading to a single convergence analysis for various methods.
result Unified convergence analysis for a wide range of SGD variants and distributed methods.
Stochastic gradient descent (SGD) is the optimization algorithm of choice in many machine learning applications such as regularized empirical risk minimization and training deep neural networks. The classical convergence analysis of SGD is carried out under the assumption that the norm of the stochastic gradient is uni…
Untuned SGD converges but with an exponential dependence on smoothness, adaptive methods prevent this.
problem The exponential dependence on smoothness in untuned SGD's convergence rate.
method Untuned SGD with arbitrary stepsize η, adaptive methods like NSGD, AMSGrad, and AdaGrad.
result Adaptive methods prevent the exponential dependence on smoothness in SGD.
Paper proposes a coupling-based diagnostic for SGD stepsize optimization.
problem Optimizing stepsize for SGD convergence.
method Coupling-based convergence diagnostic for monitoring stationarity.
result Proposed stepsize scheme achieves superior performance across convex and non-convex problems.
Simplified SGD interpretation as Ito process for broader applicability.
problem Lack of generality in current SGD interpretation.
method Introduced a simplified scheme for discrete-time approximation of Ito process.
result Flexibly interprets SGD and SGLD, providing insights into their asymptotic properties.
New study shows faster convergence of SGD and Kaczmarz methods.
problem Improving convergence rates of iterative linear system solvers.
method Last-iterate convergence analysis of SGD with greedy step size over smooth quadratics.
result The t-th iterate attains an O(1/t3/4) convergence rate.