We study a mini-batch diversification scheme for stochastic gradient descent (SGD). While classical SGD relies on uniformly sampling data points to form a mini-batch, we propose a non-uniform sampling scheme based on the Determinantal Point Process (DPP). The DPP relies on a similarity measure between data points and g…
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48 results for “mini-batch SGD”
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.
Paper finds optimal mini-batch size for SGD to speed up learning.
problem Optimizing mini-batch size for faster SGD convergence.
method Empirical inverse law and theoretical bound on mini-batch SGD training.
result An accurate model for predicting training time and identifying implications for algorithm and hardware.
In this paper we aim to formally explain the phenomenon of fast convergence of SGD observed in modern machine learning. The key observation is that most modern learning architectures are over-parametrized and are trained to interpolate the data by driving the empirical loss (classification and regression) close to zero…
Improves deep learning training by matching mini-batch distributions.
problem Overfitting and noise in mini-batch training.
method ITDM, which matches the moments of mini-batch distributions to reduce overfitting.
result ITDM reduces overfitting and improves DNN training.
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.
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…
New findings show mini-batch SGD operates in a 'Edge of Stochastic Stability' regime.
problem Understanding the stability and convergence of mini-batch SGD.
method Analyzing the mini-batch Hessian and its directional curvature.
result Mini-batch SGD operates in a different stability regime (Edge of Stochastic Stability) compared to full-batch GD.
New statistical properties for mini-batch Cox-NN optimization.
problem Optimizing deep Cox neural networks using mini-batches.
method Developed mini-batch maximum partial-likelihood estimator (mb-MPLE) for Cox-NN.
result mb-MPLE is consistent and achieves optimal convergence rate.
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…
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.
Study mini-batch SGD noise and its limits, proving complexity guarantees.
problem Analyzing the noise in mini-batch SGD and its impact on optimization.
method Examined the conditional covariance and diffusion limits of SGD under different sampling designs.
result Proved mean-square upper bounds and Fisher van Trees lower bounds for SGD, linking them to effective dimension and condition number.
Mini-batch SGD with momentum is a fundamental algorithm for learning large predictive models. In this paper we develop a new analytic framework to analyze noise-averaged properties of mini-batch SGD for linear models at constant learning rates, momenta and sizes of batches. Our key idea is to consider the dynamics of t…
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.
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.
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…
The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lowers the variance of the gradient est…
Nesterov SGD is widely used for training modern neural networks and other machine learning models. Yet, its advantages over SGD have not been theoretically clarified. Indeed, as we show in our paper, both theoretically and empirically, Nesterov SGD with any parameter selection does not in general provide acceleration o…
A new method for statistical inference using SGD under -mixing data.
problem Valid statistical inference for time series data with general correlation.
method Proposes a mini-batch SGD estimator and associated mini-batch bootstrap procedure for -mixing data.
result The proposed method constructs valid confidence intervals for -mixing data.
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.
SGD and weight decay encourage neural networks to learn low-rank weight matrices.
problem The bias of SGD towards low-rank weight matrices in neural networks.
method The study investigates the effect of SGD and weight decay on the rank of weight matrices in neural networks, both theoretically and empirically.
result Training with SGD and weight decay induces a bias towards rank minimization in weight matrices, which becomes more pronounced with smaller batch sizes and stronger weight decay.
Neural networks learn the support of the target function through SGD's implicit regularization effect.
problem Learning the support of the target function in neural networks.
method Investigation of mini-batch SGD's ability to learn the support in the first layer of a neural network.
result Mini-batch SGD effectively learns the support in the first layer by shrinking irrelevant weights, while vanilla GD requires an explicit regularization term.
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.
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient descent (SGD); but their theoretical analysis almost exclusively assumes convex…
The effective noise of Stochastic Gradient Descentcond-mat.dis-nn
Stochastic Gradient Descent introduces noise in training, affecting model decision boundaries.
problem Understanding the impact of noise in SGD on model decision boundaries.
method Characterized SGD and persistent SGD dynamics in a neural network model, measuring noise magnitude in both under- and over-parametrized regimes.
result Noisier algorithms lead to wider decision boundaries in constraint satisfaction problems.
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 bounds for KANs trained with DP-SGD, addressing correlated noise.
problem Risk bounds for Kolmogorov-Arnold Networks trained by DP-SGD with correlated noise.
method Established new optimization and population risk analysis for KANs trained with DP-SGD, addressing correlated noise.
result First optimization and population risk analysis of correlated-noise mechanisms for DP training in non-convex settings, including neural networks.
A new SGD framework reduces empirical risk by favoring higher loss observations.
problem Minimizing empirical risk in machine learning problems.
method Develops a biased gradient estimator for stochastic optimization.
result Minimizes an ordered modification of the empirical average loss.
We present a generic framework for trading off fidelity and cost in computing stochastic gradients when the costs of acquiring stochastic gradients of different quality are not known a priori. We consider a mini-batch oracle that distributes a limited query budget over a number of stochastic gradients and aggregates th…
A new GGN method speeds up training of deep neural networks for regression tasks.
problem Training deep neural networks efficiently for regression problems.
method Proposes a Gram-Gauss-Newton (GGN) algorithm for overparameterized neural networks.
result For sufficiently wide neural networks, GGN achieves quadratic convergence rate.
Differentiable learning via SGD and GD can simulate various learning problems, depending on precision and minibatch size.
problem Understanding the power of differentiable learning via SGD and GD compared to statistical query (SQ) learning.
method Comparing the learning power of SGD and GD on population and empirical losses with statistical query learning.
result The learning power of SGD and GD depends on the precision of gradient calculations relative to the minibatch size or sample size.
SGD with mini-batches can solve convex low-rank matrix problems efficiently.
problem Solving large-scale convex low-rank matrix problems efficiently.
method Stochastic Gradient Descent with mini-batches and low-rank projections.
result SGD with mini-batches produces low-rank iterates with high probability.
We propose a projected semi-stochastic gradient descent method with mini-batch for improving both the theoretical complexity and practical performance of the general stochastic gradient descent method (SGD). We are able to prove linear convergence under weak strong convexity assumption. This requires no strong convexit…
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.
Nonlinear SGD achieves high-probability rates in non-convex optimization with heavy-tailed noise.
problem Optimization in non-convex problems with heavy-tailed noise.
method General nonlinear framework for SGD, including symmetrization techniques.
result Achieves rate for heavy-tailed noise.
FSGD uses latent factors to scale SGD for high-dimensional learning.
problem Scalable optimization in high-dimensional machine learning.
method Factor-Augmented SGD (FSGD) that operates on streaming data.
result Established theoretical framework for latent factor estimation error in SGD.
74.7 seconds to train ResNet-50 on ImageNet with 2,048 GPUs.
problem Training deep learning models on large mini-batches efficiently.
method Optimization methods applied to distributed deep learning.
result Top-1 validation accuracy of 75.08% with training time of 74.7 seconds.
This work shows how exploiting gradient alignment can improve distributed and federated learning performance.
problem Misalignment of gradients across clients in distributed and federated learning.
method Utilizing implicit regularization through a novel GradAlign algorithm that induces gradient alignment with large mini-batches.
result Improvements in test accuracies and generalization performance.
What's in a Smoothness Constant? Tighter Rates for Local SGD with Bounded Second-order Heterogeneitycs.LG
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.
In this paper we focus on the problem of finding the optimal weights of the shallowest of neural networks consisting of a single Rectified Linear Unit (ReLU). These functions are of the form with denoting the weight vector. …
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.
BP-SVRG improves generalization in deep neural networks.
problem Improving generalization in deep neural networks.
method Investigates effects of mini-batching and learning rate decay on SVRG, derives BP-SVRG.
result BP-SVRG outperforms B-SVRG and SGD in deep neural networks.
Noise in SGD affects overparameterized models, favoring sparse solutions.
problem Understanding and mitigating implicit bias in SGD with parameter-dependent noise.
method Theoretical analysis of a quadratically-parameterized model with label noise and Gaussian noise.
result SGD with label noise recovers sparse ground-truth solutions, while SGD with Gaussian noise overfits dense solutions.
Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average potential over the posterior distribution of weights along with an entropic regul…
New findings show noisy gradient descent can generalize well, even with non-SGD noise.
problem The role of noise in gradient descent's generalization ability.
method Analyzed the structure of SGD noise and proposed a new noisy gradient descent algorithm.
result Noises in classes different from SGD can also effectively regularize gradient descent.
Self-paced learning and hard example mining re-weight training instances to improve learning accuracy. This paper presents two improved alternatives based on lightweight estimates of sample uncertainty in stochastic gradient descent (SGD): the variance in predicted probability of the correct class across iterations of …
New research shows many batch selection methods for training work just as well as full batch training.
problem Finding optimal batch selection methods for training.
method Analysis of mini-batch Gradient Descent (GD) and Stochastic GD (SGD) with various batch selection rules.
result All mini-batch schedules, including deterministic ones, generalize optimally for smooth Lipschitz-convex/nonconvex/strongly-convex loss functions.
This work improves SGD convergence by adaptively adjusting batch sizes.
problem High variance in gradient estimates with small batch sizes.
method Adaptive batch size adjustment based on model training loss.
result Adaptive batch size method requires fewer model updates with same computation.