Elastic Gossip distributes neural network training using gossip-like protocols.
problem Distributing neural network training across heterogeneous environments.
method Pairwise-communication using Gossip-like protocols, building on Elastic Averaging SGD.
result Elastic Gossip performs better than Gossiping SGD in experiments, but hyper-parameter search may yield better configurations.
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…
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.
Dynamic SGD improves deep learning performance in elastic distributed training.
problem Dealing with varying numbers of machines in elastic distributed training environments.
method Smoothly adjust the learning rate over time to mitigate noisy momentum estimation.
result Dynamic SGD achieves stabilized performance across different numbers of GPUs.
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.
Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.
problem Improving convergence of SGD in various settings.
method Develops a general weighted averaging scheme for SGD and establishes asymptotic normality.
result Establishes asymptotic normality and optimality of weighted averaged SGD solutions.
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.
SWALP averages SGD iterates for low-precision training, improving scalability and performance.
problem Improving scalability and performance in low-precision training.
method Averages low-precision SGD iterates with a modified learning rate schedule.
result SWALP matches full-precision SGD performance with 8-bit quantization and converges to optimal solutions.
ADPSGD optimizes SGD convergence by varying averaging periods based on model variance.
problem High communication costs in parallel SGD.
method Varying averaging period based on model variance.
result ADPSGD achieves better convergence and smaller communication compared to CPSGD.
Paper explores how combining tail-averaging and minibatching improves SGD convergence.
problem Understanding and optimizing learning properties of SGD variants.
method Least squares learning in a nonparametric setting, focusing on multiple passes, mini-batching, and averaging.
result Tail averaging allows faster convergence rates than uniform averaging in nonparametric settings.
Partial model averaging improves Federated Learning performance.
problem Periodic model averaging causes significant model discrepancy in Federated Learning.
method Proposes a partial model averaging framework that encourages local models to stay close to each other.
result Partial averaging achieves up to 2.2% higher validation accuracy than full averaging.
This work characterizes the benefits of averaging schemes widely used in conjunction with stochastic gradient descent (SGD). In particular, this work provides a sharp analysis of: (1) mini-batching, a method of averaging many samples of a stochastic gradient to both reduce the variance of the stochastic gradient estima…
Simplified analysis of SGD for linear regression with weight averaging.
problem Understanding SGD optimization in linear regression models.
method Simplified analysis using linear algebra tools, bypassing complex operator manipulations.
result Recovery of bias and variance bounds for SGD in linear regression.
SGD in linear regression overfits but performs well due to bias-variance trade-off.
problem Understanding overfitting in SGD for linear regression.
method Constant-stepsize SGD with iterate averaging or tail averaging, analyzing full eigenspectrum of data covariance matrix.
result Sharp excess risk bounds revealing bias-variance decomposition for SGD in linear regression.
New algorithm reduces communication in distributed SGD, improving efficiency.
problem Slow communication rounds bottleneck synchronous mini-batch SGD convergence.
method Proposes non-asymptotic error analysis for Local-SGD, comparing to averaging methods.
result Local-SGD reduces communication by a factor of O(√T/P^(3/2)) for large step sizes.
The paper introduces a new method to improve model generalization by routing model copies through permutations.
problem Improving model generalization in machine learning.
method The method replicates a model \(M\) times and rewire the contexts in which local learning messages are computed using permutations.
result The method improves generalization by structured message sharing rather than coupling parameters.
We derive a dimensionally-reduced limit theory for an n-dimensional nonlinear elastic body that is slender along k dimensions. The starting point is to view an elastic body as an n-dimensional Riemannian manifold together with a not necessarily isometric W1,2-immersion in n-dimensional Euclidean space. The…
A2SGD reduces distributed SGD communication to O(1) per worker.
problem Heavy communication costs in distributed SGD for large models.
method Two-level gradient averaging to consolidate gradients to two local averages.
result Achieves O(1) communication complexity per worker, significantly reducing traffic and training time.
A new distributed SGD algorithm reduces communication by infrequent global reduction.
problem Reducing communication in large-scale machine learning training.
method Hierarchical averaging stochastic gradient descent (Hier-AVG) with infrequent global reduction.
result Hier-AVG achieves comparable training speed with better test accuracy.
Local SGD with periodic averaging achieves faster convergence with less communication.
problem Communication overhead in distributed optimization.
method Local SGD with periodic averaging, Polyak-Łojasiewicz condition, adaptive synchronization.
result Local SGD can achieve linear speed up with fewer communication rounds, especially for non-strongly convex functions.
MDA optimizer performs similarly to SGD+M in CV and Adam in NLP.
problem Performance degradation due to choosing the wrong optimizer.
method Modernized Dual Averaging (MDA) optimizer, inspired by dual averaging.
result MDA performs as well as SGD+M in CV and as Adam in NLP.
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness assumptions, which do not apply to many modern applications of SGD with non-smooth object…
New insights into using momentum for non-convex optimization.
problem Improving training of non-convex models like deep neural networks.
method Developed a Lyapunov analysis of SGD with momentum using stochastic primal averaging.
result Precise conditions under which SGD+M outperforms SGD and optimal hyper-parameter schedules.
Unified analysis of finite weight averaging methods in deep learning.
problem Theoretical explanation of finite weight averaging methods in deep learning.
method Generalized SGD and LAWA, establishing convergence and generalization bounds.
result FWA achieves faster convergence and better generalization compared to SGD.
This paper analyzes SGD with increasingly weighted averaging for optimization and generalization.
problem Improving optimization and generalization for non-strongly convex objectives.
method Comprehensive analysis of increasingly weighted averaging schemes for convex, strongly convex, and non-convex objectives.
result The weight α affects both optimization and generalization errors, revealing a trade-off. 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.
Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD, with a cyclical or constant learning rate, leads to better generalization than conv…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are statistically inefficient as estimators of the true parameter value. To address these tw…
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.
The paper analyzes time-dependent streaming data with biased gradient estimates and proposes improved stochastic optimization methods.
problem Stochastic optimization in a streaming setting with time-dependent and biased gradient estimates.
method Analysis of several first-order methods including SGD, mini-batch SGD, and time-varying mini-batch SGD, along with their Polyak-Ruppert averages.
result Time-varying mini-batch SGD methods can break long- and short-range dependence structures, and biased SGD methods can achieve comparable performance to their unbiased counterparts.
New method averages SGD iterates to achieve adjustable regularization.
problem Overfitting in machine learning models.
method Averaging SGD iterates for regularized solutions.
result Obtain regularized solutions without tuning parameters.
The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied nonconvex loss functions, but only considered the generalization error of the SGD in…
Consider a number of workers running SGD independently on the same pool of data and averaging the models every once in a while -- a common but not well understood practice. We study model averaging as a variance-reducing mechanism and describe two ways in which the frequency of averaging affects convergence. For convex…
Although stochastic gradient descent (SGD) method and its variants (e.g., stochastic momentum methods, AdaGrad) are the choice of algorithms for solving non-convex problems (especially deep learning), there still remain big gaps between the theory and the practice with many questions unresolved. For example, there is s…
We present a novel method for frequentist statistical inference in M-estimation problems, based on stochastic gradient descent (SGD) with a fixed step size: we demonstrate that the average of such SGD sequences can be used for statistical inference, after proper scaling. An intuitive analysis using the Ornstein-Uhlen…
New framework analyzes SGD dynamics in large samples and dimensions.
problem Analyzing stochastic gradient descent in large-scale settings.
method Inspired by random matrix theory, new framework for fixed stepsize and finite sum settings.
result SGD dynamics become deterministic in the large sample and dimensional limit, governed by a Volterra integral equation.
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.
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.
SGDM accelerates faster than SGD with large batch sizes and permits broader learning rates.
problem Understanding the role of momentum in SGDM and its convergence rates.
method Analysis of SGDM convergence rates under strongly convex settings, including finite-sample rates and asymptotic normality of the averaged estimator.
result SGDM converges faster than SGD with large batch sizes and permits broader learning rates.
New stability analysis improves generalization of multipass SGD.
problem Improper preconditioning affects generalization in multipass SGD.
method Developed on-average stability analysis for multipass SGD.
result Proper preconditioning yields optimal effective dimension dependence.
Deformation estimation of elastic object assuming an internal organ is important for the computer navigation of surgery. The aim of this study is to estimate the deformation of an entire three-dimensional elastic object using displacement information of very few observation points. A learning approach with a neural net…
Behavior cloning training instabilities amplified by SGD noise over long horizons.
problem Training instabilities in behavior cloning with deep neural networks.
method Empirical dissection of minibatch SGD updates and their effects on long-horizon rewards.
result Exponential moving average (EMA) of iterates effectively mitigates gradient variance amplification (GVA).
We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the p…
Non-asymptotic rates for SGD via martingale CLT.
problem Improving the convergence rates of SGD.
method Combining Stein's method and Lindeberg's argument for multivariate martingale CLT, then applying to SGD.
result Explicit rates for multivariate martingale CLT and SGD convergence.
AdaComm optimizes SGD by dynamically adjusting communication frequency for faster convergence.
problem Achieving optimal error-runtime trade-off in distributed SGD.
method Adaptive communication strategy that starts with infrequent averaging to save delay and improve speed, then increases frequency.
result AdaComm reduces training time by 3x while maintaining the same final loss.
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust …
The paper provides statistical guarantees for SGD and ASGD in high-dimensional settings.
problem Theoretical understanding of SGD and ASGD in high-dimensional settings.
method Transfer of tools from high-dimensional time series to online learning, using coupling techniques.
result Established geometric-moment contraction and q-th moment convergence of SGD and ASGD. We introduce a simple algorithm, True Asymptotic Natural Gradient Optimization (TANGO), that converges to a true natural gradient descent in the limit of small learning rates, without explicit Fisher matrix estimation. For quadratic models the algorithm is also an instance of averaged stochastic gradient, where the par…