SGD without replacement decouples into curvature-following and flatness-regularizing steps.
problem Theoretical analysis of SGD without replacement for large-scale neural networks.
method Analysis of SGD without replacement in a realistic regime, considering high curvature and flatness.
result Optimizing with SGD without replacement is locally equivalent to an additional regularizer step.
Paper closes convergence gap for SGD without replacement.
problem Establishing convergence rate for SGD without replacement.
method Analyzes convergence rates for strongly convex and smooth functions.
result Achieves a rate of O(1/T^2 + n^2/T^3) for quadratic sums.
Differential privacy is a useful tool to build machine learning models which do not release too much information about the training data. We study the Rényi differential privacy of stochastic gradient descent when each training example is sampled without replacement (also known as cyclic SGD). Cyclic SGD is typically f…
We study stochastic gradient descent {\em without replacement} (\sgdwor) for smooth convex functions. \sgdwor is widely observed to converge faster than true \sgd where each sample is drawn independently {\em with replacement} \cite{bottou2009curiously} and hence, is more popular in practice. But it's convergence prope…
Stochastic Gradient Descent underperforms on some problems, contrary to expectations.
problem Understanding the generalization performance of SGD on specific problem instances.
method Analysis of stochastic convex optimization framework, proving empirical and generalization gaps for SGD.
result SGD exhibits both empirical risk and generalization gap of Ω(1) on some problem instances, contradicting its conventional understanding. 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.
While machine learning has achieved remarkable results in a wide variety of domains, the training of models often requires large datasets that may need to be collected from different individuals. As sensitive information may be contained in the individual's dataset, sharing training data may lead to severe privacy conc…
A long-standing problem in the theory of stochastic gradient descent (SGD) is to prove that its without-replacement version RandomShuffle converges faster than the usual with-replacement version. We present the first (to our knowledge) non-asymptotic solution to this problem, which shows that after a "reasonable" numbe…
Optimal SGD rates achieved with shuffling, covering non-convex and convex cases.
problem Optimizing finite-sum optimization problems with shuffling strategies.
method RandomShuffle and SingleShuffle algorithms for SGD, analyzing convergence rates.
result Minimax optimal convergence rates established, generalizing to non-convex costs.
The paper analyzes the variance of different shuffling methods in stochastic gradient descent.
problem Understanding the variance of different shuffling methods in stochastic gradient descent.
method Power spectral density analysis to study the noise sequences of stochastic gradients.
result The stationary variances of iterates decrease in the order of SGD, SGD-RR, and SGD-SO.
Stochastic Gradient Descent (SGD) is a central tool in machine learning. We prove that SGD converges to zero loss, even with a fixed (non-vanishing) learning rate - in the special case of homogeneous linear classifiers with smooth monotone loss functions, optimized on linearly separable data. Previous works assumed eit…
Improved rates for continual learning using SGD and last-iterate analysis.
problem Forgetting in overparameterized models after fitting multiple tasks.
method Developed novel SGD upper bounds for continual linear models and analyzed their performance.
result Established universal forgetting rates for continual learning.
New bounds for SGD show improved performance in various settings.
problem Improving convergence bounds for SGD with random permutations.
method Analyzing convergence of SGD with random reshuffling and arbitrary permutations.
result Tighter lower bounds for weighted average iterates in both convex and strongly-convex cases.
We propose a reduction for non-convex optimization that can (1) turn an stationary-point finding algorithm into an local-minimum finding one, and (2) replace the Hessian-vector product computations with only gradient computations. It works both in the stochastic and the deterministic settings, without hurting the algor…
New insights into privacy guarantees for subsampled mechanisms under composition.
problem Tight privacy guarantees for the composition of subsampled differentially private mechanisms.
method Addressed confusion points in privacy accounting for subsampled mechanisms, providing examples and counterexamples.
result Privacy guarantees for subsampled mechanisms differ significantly between Poisson subsampling and sampling without replacement.
New method shows hidden state can significantly improve differential privacy in SGD.
problem Differential privacy in SGD with hidden state.
method Proves converging privacy bounds for hidden state SGD, using privacy amplification techniques.
result Privacy bound converges exponentially fast and is smaller than composition bounds.
SMD outperforms SGD in over-parametrized linear models for certain data distributions.
problem Understanding the generalization performance of SMD in over-parametrized linear models.
method Analysis of SMD for over-parametrized linear models with binary classification.
result Empirical validation of SMD's generalization performance differing from SGD.
Random permutations can offer faster convergence than with-replacement sampling for some functions.
problem Understanding when and how random permutations outperform with-replacement sampling in SGD convergence.
method Analyzing convergence rates for different function classes (1D strongly convex, general strongly convex, quadratic strongly convex).
result The optimal convergence gap between random and permutation-based SGD varies from exponential to nonexistent, depending on the function class.
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.
New analysis for black-box learning without gradients, improving generalization bounds.
problem Generalization error analysis for derivative-free optimization.
method Zeroth-order Stochastic Search (ZoSS) algorithm for Lipschitz and smooth losses.
result Generalization bounds independent of model dimension, batch size, and number of perturbed evaluations.
Cheap methods improve uncertainty in SGD solutions.
problem Uncertainty quantification in SGD solutions.
method Two resampling-based methods: parallel resampling with replacement and online resampling.
result Significantly reduced computation effort in constructing confidence intervals.
Smoothed SGD improves quantile estimation without crossing curves.
problem Estimating quantiles without crossing estimated curves.
method Smoothed SGD algorithm with Bahadur representation and Gaussian approximation.
result Smoothed SGD provides non-asymptotic tail probability bounds and a Gaussian approximation for quantile estimates.
Efficiently samples sequences without replacement for machine learning models.
problem Generating diverse outputs from sequential models without duplicates.
method Incremental sampling procedure for randomized programs, including neural models.
result Efficacy and flexibility of incremental sampling for large output spaces.
Mixed-precision CA-SGD for generalized linear models on GPUs
problem SGD communication bottleneck
method Mixed-precision CA-SGD
result Matches FP32 SGD loss within 0.5% on various problems
We investigate the dynamical and convergent properties of stochastic gradient descent (SGD) applied to Deep Neural Networks (DNNs). Characterizing the relation between learning rate, batch size and the properties of the final minima, such as width or generalization, remains an open question. In order to tackle this pro…
Minibatch SGD outperforms Local SGD in heterogeneous distributed learning.
problem Optimizing a combined convex objective with stochastic gradient estimates from different machines.
method Analysis of Minibatch SGD and Local SGD in a heterogeneous distributed setting.
result Minibatch SGD dominates Local SGD in the heterogeneous distributed setting.
Paper explores whether gradient normalization can replace clipping for SGD in heavy-tailed noise.
problem Ensuring convergence of SGD in heavy-tailed noise.
method Revisits gradient clipping and normalization, proving their sufficiency and effectiveness.
result Gradient normalization alone is sufficient for nonconvex SGD convergence under smoothness assumptions.
IntSGD compresses SGD gradients without floats, converging as SGD.
problem Efficiently compressing stochastic gradients in distributed SGD.
method Adaptive integer compression of gradients, estimating scaling adaptively.
result IntSGD matches SGD's iteration complexity for convex and non-convex functions.
SRSGD improves DNN training speed and accuracy.
problem Training deep neural networks is computationally expensive and slow.
method Scheduled Restart SGD (SRSGD) combines NAG momentum with momentum reset.
result SRSGD achieves better error rates with fewer training epochs.
Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing theoretical results for SGD applied to nonconvex objective functions are far from …
Artificial intelligence is revolutionizing our lives at an ever increasing pace. At the heart of this revolution is the recent advancements in deep neural networks (DNN), learning to perform sophisticated, high-level tasks. However, training DNNs requires massive amounts of data and is very computationally intensive. G…
New stability bounds for SGD on nonsmooth convex losses.
problem Understanding stability of SGD on nonsmooth convex losses.
method Sharp upper and lower bounds for SGD and full-batch GD on nonsmooth convex losses.
result SGD can be less stable but still useful for generalization bounds.
The Lookahead optimizer improves SGD's performance and generalization without restrictive assumptions.
problem Improving the generalization of SGD with Lookahead.
method A rigorous stability and generalization analysis of the Lookahead optimizer with minibatch SGD, leveraging on-average model stability.
result Derives generalization bounds for convex and strongly convex problems without the restrictive Lipschitzness assumption, demonstrating a linear speedup with batch size.
Paper analyzes how EMA improves SGD in linear regression.
problem Understanding the effectiveness of EMA in training deep learning models.
method Established risk bound for online SGD with EMA in linear regression.
result SGD with EMA has smaller variance error and exponentially decaying bias error.
New proof shows D-SGD and SAM are equivalent, revealing advantages of decentralization.
problem The generalization benefits of decentralized learning.
method Proved D-SGD implicitly minimizes SAM's loss function.
result Decentralized SGD and Average-direction SAM are asymptotically equivalent.
New method improves scalability of SGD for large datasets.
problem High variance in stochastic gradient descent.
method Adaptive measure reduction with Carathéodory's theorem.
result Improved scalability to high-dimensional spaces.
Sampling without replacement speeds up optimization in minimax problems.
problem Optimizing minimax problems with faster convergence rates.
method Analysis of gradient descent ascent and proximal point method with two sampling strategies.
result Sampling without replacement leads to faster convergence rates in minimax optimization.
Large batch training with DP-SGD reduces model performance due to implicit bias.
problem Large batch training with DP-SGD reduces model performance.
method The study analyzes the phenomenon of implicit bias in Noisy-SGD (DP-SGD without clipping) and its theoretical solutions for linear models.
result The implicit bias in large batch training with DP-SGD is amplified by additional noise, similar to SGD.
We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific probability law governing the data selection rule used to form mini-batches. This is…
The well-known Gumbel-Max trick for sampling from a categorical distribution can be extended to sample k elements without replacement. We show how to implicitly apply this 'Gumbel-Top-k' trick on a factorized distribution over sequences, allowing to draw exact samples without replacement using a Stochastic Beam Sea…
Due to its efficiency and ease to implement, stochastic gradient descent (SGD) has been widely used in machine learning. In particular, SGD is one of the most popular optimization methods for distributed learning. Recently, quantized SGD (QSGD), which adopts quantization to reduce the communication cost in SGD-based di…
AdaGrad-Norm achieves optimal convergence rates for non-convex objectives without tuning.
problem Optimal convergence rates for non-convex, smooth objectives with adaptive step sizes.
method Adaptive SGD (AdaGrad-Norm) with self-tuning step sizes, analyzing under unbounded gradients and affine variance scaling.
result AdaGrad-Norm achieves order optimal convergence rate of $\mathcal{O}\left(\frac{\mathrm{poly}\log(T)}{\sqrt{T}}
ight)$ under optimal assumptions.
We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show that - contrary to the case of isotropic noise - this variance is proportional to t…
Privacy-preserving SGD with heavy-tailed noise achieves differential privacy guarantees.
problem Privacy preservation in noisy SGD with heavy-tailed noise.
method Differential privacy guarantees for SGD with heavy-tailed noise.
result SGD with heavy-tailed perturbations achieves (0,O(1/n))-DP. Introduces a new stochastic optimization method for deep learning.
problem Minimizing loss functions in deep neural networks.
method Introduces a second-order stochastic Runge-Kutta method and an adaptive SGD-G2.
result The method yields consistent minimization of loss functions and automatically adjusts learning rates.
When using stochastic gradient descent to solve large-scale machine learning problems, a common practice of data processing is to shuffle the training data, partition the data across multiple machines if needed, and then perform several epochs of training on the re-shuffled (either locally or globally) data. The above …
DP-SGD can update fewer coordinates while maintaining privacy.
problem How to update fewer coordinates in DP-SGD without losing optimization signal.
method TP-TopK (Two-Phase TopK DP-SGD), a two-phase method for coordinate-sparse private training.
result Private training can update fewer coordinates without losing optimization signal, scaling noise with active dimension \(k\) instead of full dimension \(d\).
New PAC-Bayes bounds use Wasserstein distances to improve generalization.
problem Lack of geometric properties in existing PAC-Bayes bounds.
method Developed new PAC-Bayes bounds with Wasserstein distances.
result Optimization guarantees translate to good generalization abilities.