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.
Develops anytime-valid stopping rules for SGD based on observed trajectory.
problem Stopping stochastic gradient descent (SGD) based on observed trajectory.
method Develops anytime-valid confidence sequences for stochastic gradient methods.
result Statistically valid, time-uniform stopping rules for SGD across convex and nonconvex settings.
Ringmaster ASGD improves Asynchronous SGD's efficiency under varying worker times.
problem Suboptimal performance of Asynchronous SGD under heterogeneous worker computation times.
method Ringmaster ASGD, a novel Asynchronous SGD method with optimal time complexity.
result Ringmaster ASGD achieves optimal time complexity under arbitrary worker heterogeneity.
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.
Layer-wise preconditioning methods improve neural network optimization and feature learning.
problem Suboptimal feature learning in standard optimization algorithms.
method Layer-wise preconditioning methods that introduce preconditioners per axis of each layer's weight tensors.
result Layer-wise preconditioning is necessary for provable feature learning in linear and single-index models.
Momentum SGD fails to track nonstationary optima due to drift amplification.
problem Tracking nonstationary optima in stochastic optimization.
method Theoretical analysis of SGD and momentum variants under strong convexity and smoothness.
result Momentum incurs a drift-amplification penalty that diverges as the momentum parameter approaches 1, leading to systematic lag.
GD outperforms ridge regression and SGD in linear regression problems.
problem Comparing the risks of GD, ridge regression, and SGD in linear regression problems.
method Instance-wise finite-sample risk analysis of GD, ridge regression, and SGD.
result GD outperforms ridge regression and is incomparable with SGD in some cases.
Stochastic Gradient Descent shows directional bias with moderate learning rates, impacting optimization outcomes.
problem Understanding the bias of SGD with moderate learning rates in practical scenarios.
method Analyzing SGD and GD on an overparameterized linear regression problem.
result SGD converges along large eigenvalue directions, GD along small ones, affecting early stopping outcomes.
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…
Study on adversarial training dynamics in high dimensions using SGD.
problem Analyzing adversarial training of models in high-dimensional settings.
method Deriving deterministic equivalents for SGD iterates under Gaussian mixtures.
result No constant learning rate guarantees monotone descent in adversarial training.
Improved SGD bounds for machine learning models with Markovian noise.
problem Uniform high-probability bounds for SGD under PL condition with Markovian noise.
method Combining Poisson equation for Markovian noise and probabilistic induction for almost-sure bounds.
result Matching 1/k decay rate for expected suboptimality. Paper proves suboptimal convergence rate of last iterate for SGDM.
problem Proves suboptimal convergence rate of last iterate for SGDM.
method Focuses on convergence rate of last iterate of SGDM, introduces Follow-The-Regularized-Leader-based algorithms.
result Shows optimal convergence rate of last iterate for unconstrained convex stochastic optimization problems.
Noise in SGD helps deep nets generalize better, even with smaller batch sizes.
problem The generalization benefit of using noise in SGD over large batch sizes.
method Carefully designed experiments and rigorous hyperparameter sweeps on various models.
result Small or moderately large batch sizes outperform very large batches on test sets.
This work improves online SGD's sample complexity for multi-index models by considering higher-order terms.
problem Suboptimal sample complexity for learning multi-index models using online SGD.
method Focus on both second- and higher-order terms to improve sample complexity.
result Online SGD achieves ildeO(dPL−1) samples for multi-index models. New sampling scheme improves privacy in DP-SGD without sacrificing utility.
problem Suboptimal privacy amplification due to participation variance in Poisson subsampling.
method Balanced Iteration Subsampling (BIS) with structured randomness.
result BIS achieves stronger privacy amplification than Poisson subsampling and is optimal at both extremes of noise spectrum.
Deep neural networks are usually trained with stochastic gradient descent (SGD), which minimizes objective function using very rough approximations of gradient, only averaging to the real gradient. Standard approaches like momentum or ADAM only consider a single direction, and do not try to model distance from extremum…
New algorithms improve SGD convergence and reduce variance for over-parameterized models.
problem Slower convergence in non-interpolation settings for SGD variants.
method Proposed AdaSPS and AdaSLS with variance reduction for robust convergence.
result Achieves faster convergence rates and robustness in non-interpolation settings.
Adam avoids simplicity bias in neural networks, leading to better generalization.
problem Simplicity bias in neural networks trained with SGD.
method Comparison of Adam and GD on binary classification tasks with Gaussian data.
result Adam leads to richer and more diverse features, improving generalization.
Optimizes sparse fine-tuning for privacy in neural networks.
problem Performance gap between DP-SGD and non-private fine-tuning.
method Optimization-based approach using private gradient information for selecting trainable weights.
result Our selection method leads to better prediction accuracy compared to existing approaches.
Novel algorithm reduces privacy noise in machine learning.
problem High privacy noise in machine learning algorithms.
method Robust statistics, specifically median and trimmed mean, to bound sensitivity of SGD iterates.
result Improved privacy-utility trade-off with reduced noise and computational efficiency.
Two entropy measures quantify suboptimal portfolio performance.
problem Measuring suboptimality in investment portfolios.
method Relative entropy (KL divergence) calculations.
result Suboptimal portfolios appear better than Kelly portfolios under certain measures.
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.
Novel IRL method identifies suboptimal medical decisions in ICU data.
problem Identifying suboptimal medical decisions in clinical settings.
method Incorporates Inverse Reinforcement Learning with a pruning step to identify and remove suboptimal actions.
result Pruning step effectively identifies clinical priorities and values from suboptimal data.
Guarantees convergence for black-box variational inference without modifications.
problem Convergence guarantees for black-box variational inference.
method Analysis of log-smooth posterior densities, location-scale variational family, and convergence rates of algorithm design choices.
result Proximal stochastic gradient descent fixes suboptimal convergence rates and achieves strongest known guarantees.
Stochastic gradient descent (SGD) is a popular stochastic optimization method in machine learning. Traditional parallel SGD algorithms, e.g., SimuParallel SGD, often require all nodes to have the same performance or to consume equal quantities of data. However, these requirements are difficult to satisfy when the paral…
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.
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-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 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.
Homogenized SGD explains SGD dynamics in high dimensions.
problem Understanding SGD dynamics in high-dimensional settings.
method Developed a homogenized SGD model to analyze high-dimensional SGD.
result Convergent high-dimensional SGD to homogenized SGD for quadratic statistics.
MindFlayer SGD improves parallel SGD for heterogeneous, random compute times.
problem Minimizing nonconvex functions with heterogeneous, random compute times.
method MindFlayer SGD, designed for stochastic and heterogeneous delays.
result MindFlayer SGD outperforms existing methods in environments with heavy-tailed noise.
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.
New suboptimal algorithm for best subset selection in high-dimensional data.
problem Nonconvex and computationally challenging best subset selection in linear regression.
method Introducing a new suboptimal algorithm and comparing it with other popular methods.
result The new procedure is a competitive suboptimal algorithm for high-dimensional data.
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.
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.
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…
New analysis improves sample complexity for vanilla policy gradient methods.
problem Improving sample complexity guarantees for vanilla policy gradient methods.
method Adapting tools from SGD analysis to policy gradient methods, with smoothness and gradient approximation assumptions.
result Established improved sample complexity bounds for convergence and global optimum.
VRL-SGD reduces communication complexity in non-identical data settings.
problem Training machine learning models with non-identical data distribution.
method VRL-SGD, which eliminates gradient variance dependency and achieves linear speedup with lower communication complexity.
result VRL-SGD reduces communication complexity from $O(T^{ rac{3}{4}} N^{ rac{3}{4}})$ to $O(T^{ rac{1}{2}} N^{ rac{3}{2}})$.
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.
New bounds for M-SGD show its error distribution is nearly Gaussian.
problem Understanding the error distribution of M-SGD.
method Proved non-asymptotic bounds for M-SGD in Wasserstein distance.
result Error distribution of M-SGD is approximately Gaussian.
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.
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.
Stochastic Gradient Descent (SGD) is the most popular algorithm for training deep neural networks (DNNs). As larger networks and datasets cause longer training times, training on distributed systems is common and distributed SGD variants, mainly asynchronous and synchronous SGD, are widely used. Asynchronous SGD is com…
AdaSGD combines SGD and Adam benefits, eliminating the need for transition.
problem Understanding when to transition from Adam to SGD for optimal performance.
method Adapting a single global learning rate for SGD (AdaSGD).
result AdaSGD combines the benefits of both SGD and Adam, improving convergence and generalization.
To reduce the long training time of large deep neural network (DNN) models, distributed synchronous stochastic gradient descent (S-SGD) is commonly used on a cluster of workers. However, the speedup brought by multiple workers is limited by the communication overhead. Two approaches, namely pipelining and gradient spar…
New insights into SGD and SGD-M in high dimensions.
problem Understanding and comparing SGD and SGD-M in high-dimensional settings.
method Developed high-dimensional scaling limits for SGD-M and online SGD, examining their dynamics and performance.
result SGD-M amplifies high-dimensional effects, potentially degrading performance compared to online SGD.
SGD outperforms GD in high dimensions via implicit conditioning, revealed by asymptotic analysis.
problem Understanding why SGD outperforms GD in high-dimensional convex problems.
method Asymptotic analysis of multi-pass SGD on high-dimensional convex quadratics, establishing an equivalence to HSGD.
result SGD's efficiency is explained by implicit conditioning, not regularization.