Local SGD outperforms minibatch SGD for quadratic objectives.
problem Theoretical foundations of local SGD are lacking.
method Proved local SGD strictly dominates minibatch SGD for quadratic objectives and accelerated local SGD is minimax optimal.
result Local SGD does not dominate minibatch SGD in general convex objectives.
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 shows local SGD outperforms mini-batch SGD under certain conditions.
problem Proving local SGD's superiority in distributed learning with heterogeneous data.
method New lower and upper bounds for local SGD under first-order heterogeneity assumptions.
result Local SGD is min-max optimal under certain conditions, resolving understanding of distributed optimization.
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.
STL-SGD accelerates Local SGD by gradually increasing communication periods.
problem Reducing communication complexity in distributed SGD.
method Gradually increasing communication periods while decreasing learning rate.
result Significant reduction in communication complexity with improved convergence rates.
Communication bottleneck has been identified as a significant issue in distributed optimization of large-scale learning models. Recently, several approaches to mitigate this problem have been proposed, including different forms of gradient compression or computing local models and mixing them iteratively. In this paper…
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.
New analysis shows Local SGD can achieve error scaling with only fixed number of communications.
problem Speeding up SGD by parallelizing across multiple workers with reduced communication overhead.
method Proposed and analyzed Local SGD method with a fixed number of communications independent of the number of steps.
result Achieves an error scaling as 1/(nT) with only a fixed number of communications (Ω(n)).
Overlap-Local-SGD improves distributed SGD by overlapping communication and computation.
problem High communication delay and node slowdown in distributed SGD.
method Adding an anchor model to synchronize local updates and pull them towards the anchor model.
result Overlap-Local-SGD speeds up distributed training and mitigates straggler effects.
Local SGD outperforms conventional methods in LLM training.
problem Training large language models on distributed devices.
method Local SGD algorithm applied to distributed training.
result Local SGD achieves competitive results in LLM training.
To accelerate the training of machine learning models, distributed stochastic gradient descent (SGD) and its variants have been widely adopted, which apply multiple workers in parallel to speed up training. Among them, Local SGD has gained much attention due to its lower communication cost. Nevertheless, when the data …
This paper analyzes Local SGD for federated learning, achieving both statistical and communication efficiency.
problem Statistical estimation and inference in federated learning with decentralized data.
method Local SGD, a multi-round estimation procedure using intermittent communication.
result Local SGD achieves both statistical efficiency and communication efficiency.
We provide a new analysis of local SGD, removing unnecessary assumptions and elaborating on the difference between two data regimes: identical and heterogeneous. In both cases, we improve the existing theory and provide values of the optimal stepsize and optimal number of local iterations. Our bounds are based on a new…
Study on the noise in SGD minibatches near local minima.
problem Understanding the noise in SGD minibatches near local minima.
method Detailed analysis of SGD noise in linear regression and derivation of a general formula for different types of minima.
result Provides insight into the stability of training neural networks and suggests large learning rates can help generalization.
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…
The paper provides Gaussian approximations for decentralized Federated Learning.
problem Lack of asymptotic statistical guarantees for local SGD in Federated Learning.
method Two generalized Gaussian approximation results for local SGD trajectories.
result Valid multiplier bootstrap procedures and Gaussian bootstrap-based tests for detecting adversarial attacks.
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.
Truncated SGD with heavy-tailed noise eliminates sharp local minima.
problem Avoiding sharp local minima in deep learning models.
method Truncated SGD with heavy-tailed gradient noise.
result Truncated SGD can eliminate sharp local minima entirely from its training trajectory.
Local SGD proves efficient in overparameterized linear regression.
problem Efficiently learning overparameterized linear models in distributed settings.
method Distributed SGD (DSGD) with overparameterized models.
result Excess risk of SGD is smaller than ridge regression in the same sample complexity.
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.
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.
Recently, the technique of local updates is a powerful tool in centralized settings to improve communication efficiency via periodical communication. For decentralized settings, it is still unclear how to efficiently combine local updates and decentralized communication. In this work, we propose an algorithm named as L…
Study of SGD with state-dependent noise, improving escape from local minima.
problem Understanding and improving the dynamics of SGD in non-convex optimization.
method Formal study on SGD with state-dependent noise, proposing power-law dynamic with state-dependent diffusion.
result Power-law dynamic can escape from sharp minima exponentially faster than flat minima.
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.
CSER improves SGD efficiency by resetting errors and partial synchronization.
problem Limited scalability of Distributed Stochastic Gradient Descent (SGD) due to communication bottlenecks.
method Introduces 'error reset' technique and partial synchronization for gradients and models.
result Proves convergence for smooth non-convex problems and accelerates distributed training significantly.
New insights into optimizing Local SGD's outer optimizer for faster convergence.
problem Understanding the impact of outer optimizer and its hyperparameters in Local SGD.
method Analyzing convergence guarantees with new outer learning rates and momentum.
result Tuning the outer learning rate can improve convergence and handle inner learning rate ill-tuning.
A distributed SGD method for heterogeneous networks with hubs and workers.
problem Learning in heterogeneous multi-level networks with worker heterogeneity and varying communication.
method Multi-Level Local SGD: distributed SGD with hub-and-spoke paradigm and hub averaging.
result The method converges with error dependent on worker heterogeneity, hub network topology, and iterations.
FedSel uses local differential privacy to protect data privacy in federated SGD.
problem Privacy leakage from gradients in federated SGD.
method Two-stage framework with top-k dimension selection and gradient accumulation.
result FedSel reduces privacy leakage by privately selecting important dimensions.
Averaged SGD optimizes a smoothed objective, leading to better generalization.
problem Improving generalization performance in machine learning models.
method Analyzed the smoothed objective function of SGD and proved that averaged SGD can optimize this smoothed function efficiently.
result Averaged SGD can efficiently optimize a smoothed objective, leading to better generalization.
This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenval…
SGD's escape rate depends on log loss barrier, not linear loss barrier.
problem Understanding the escape rate of SGD from local minima.
method Derived a stochastic differential equation (SDE) with additive noise from SGD's multiplicative noise property.
result The log loss barrier determines the escape rate of SGD, not the linear loss barrier.
Multi-layer neural networks are among the most powerful models in machine learning, yet the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a non-convex high-dimensional objective (risk function), a problem which is usually attacked using stochastic g…
Communication overhead is one of the key challenges that hinders the scalability of distributed optimization algorithms. In this paper, we study local distributed SGD, where data is partitioned among computation nodes, and the computation nodes perform local updates with periodically exchanging the model among the work…
Mini-batch stochastic gradient methods (SGD) are state of the art for distributed training of deep neural networks. Drastic increases in the mini-batch sizes have lead to key efficiency and scalability gains in recent years. However, progress faces a major roadblock, as models trained with large batches often do not ge…
SGD generalization bounds derived from information theory.
problem Understanding generalization of SGD for non-convex functions.
method Combining information-theoretic bounds with perturbation analysis.
result Upper bounds on SGD's generalization error based on gradient variance and function smoothness.
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.
This research explains why SGD generalizes better than ADAM in deep learning.
problem Understanding the generalization gap between SGD and ADAM in deep learning.
method Analyzing local convergence behaviors through Levy-driven stochastic differential equations (SDEs).
result SGD is more locally unstable and better escapes from sharp minima to flatter ones, leading to better generalization.
Hogwild! adapts to distributed data by varying mini-batch sizes.
problem Efficiently parallelize SGD over distributed local data sets.
method Asynchronous SGD with varying mini-batch sizes, aggregated by an aggregator.
result Improved convergence for heterogeneous data, reducing communication rounds.
New insights into SGD and generalization via shift-curvature and bias-curvature mechanisms.
problem Understanding the role of curvature in generalization and how SGD affects it.
method Derivation of new SGD steady-state distribution and analysis of shift-curvature and bias-curvature mechanisms.
result Shift-curvature is a significant factor in test performance, especially for small SGD noise.
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.
New study shows deep networks generalize well due to loss surface geometry.
problem Why deep networks generalize well despite many parameters.
method Analyzed local geometry of loss surface and its effect on SGD.
result SGD stays close to low-dimensional subspace, leading to better generalization bounds.
In this paper, we propose and analyze SPARQ-SGD, which is an event-triggered and compressed algorithm for decentralized training of large-scale machine learning models. Each node can locally compute a condition (event) which triggers a communication where quantized and sparsified local model parameters are sent. In SPA…
SGD can jump from high rank minima to low rank minima in DLNs, but not back.
problem SGD's tendency to get stuck in high rank minima in DLNs.
method Analysis of the L2-regularized loss function of DLNs and the definition of absorbing sets. result SGD has a non-zero probability to jump from high rank minima to low rank minima but zero probability to jump back.
Heavy-tailed distributions emerge in SGD's parameter evolution.
problem Understanding heavy-tailed distributions in SGD parameter evolution.
method Continuous diffusion approximation of SGD (homogenized SGD) analysis.
result Explicit upper and lower bounds on tail-index of homogenized SGD.
A(DP)2SGD improves federated learning privacy and efficiency.
problem Privacy and efficiency in federated learning with asynchronous decentralized parallel SGD.
method Differentially private asynchronous decentralized parallel SGD (A(DP)2SGD) using R{é}nyi differential privacy. result Achieves optimal convergence rate and comparable model accuracy to SSGD but faster.
We design a stochastic algorithm to train any smooth neural network to ε-approximate local minima, using O(ε−3.25) backpropagations. The best result was essentially O(ε−4) by SGD. More broadly, it finds ε-approximate local minima of any smooth nonconvex function in …
Stochastic gradient descent (SGD) is a well known method for regression and classification tasks. However, it is an inherently sequential algorithm at each step, the processing of the current example depends on the parameters learned from the previous examples. Prior approaches to parallelizing linear learners using SG…
Deep learning dynamics exhibit anomalous superdiffusion initially, aiding escape from local minima.
problem Understanding the dynamics of learning in deep neural networks.
method Novel analysis of SGD dynamics and loss landscape structure.
result SGD exhibits anomalous superdiffusion initially, transitioning to subdiffusion as learning progresses.