SGD noise has no bias advantage in online learning, contrary to offline learning.
problem The role of SGD noise in online learning.
method Extensive empirical analysis of image and language data.
result Small batch sizes do not confer any implicit bias advantages in online learning.
Paper proposes an online estimator for covariance matrix of SGD iterates.
problem Quantifying variability and randomness of SGD-based estimates in online learning.
method Proposes a fully online estimator for covariance matrix of ASGD using SGD iterates.
result Establishes consistency of the online estimator and shows comparable convergence rate to offline methods.
New CLT for SGD in high-dimensional regression provides online inference.
problem Quantifying uncertainty in SGD for high-dimensional regression.
method Established a high-dimensional CLT for online SGD iterates.
result Developed an online approach for estimating variance in CLT.
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.
Schedule-free SGD is optimal for nonconvex optimization problems.
problem Nonconvex optimization in neural networks.
method Developed a general framework for online-to-nonconvex conversion, which converts schedule-free SGD into an effective nonconvex optimization algorithm.
result Schedule-free SGD achieves optimal iteration complexity for nonsmooth, nonconvex optimization problems.
New bounds for SGD in high dimensions improve inference efficiency.
problem Quantifying uncertainty in high-dimensional SGD.
method Established non-asymptotic Berry--Esseen bounds for online least-squares SGD.
result Gaussian Central Limit Theorem holds for t ≳ d 1 + δ t \gtrsim d^{1+δ} t ≳ d 1 + δ , extending dimensional scaling. New method for online inference using SGD with random scaling.
problem Efficient online inference for SGD parameters.
method Asymptotic pivotal statistics via random scaling.
result Robust and efficient online inference without resampling.
A method for efficient statistical inference from online algorithms.
problem Computational constraints in online algorithms make traditional variance estimation difficult.
method HulC method that wraps around online algorithms to produce valid confidence regions.
result The HulC method produces asymptotically valid confidence regions for online algorithms.
A new algorithm combines SGD and Thompson Sampling for contextual bandits.
problem Finding efficient algorithms for contextual bandits with low time and memory complexity.
method Online Stochastic Gradient Descent (SGD) combined with Thompson Sampling.
result Achieves i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret with linear time complexity in T T T and d d d . Two new covariance estimators for ROOT-SGD improve statistical inference.
problem Uncertainty measurement for ROOT-SGD's normal distribution estimator.
method Developed two covariance estimators: plug-in and Hessian-free.
result Hessian-free estimator is asymptotically consistent and Hessian-free.
Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time step. First, we show that SGD can be used to learn the best possible sampling distr…
This work analyzes DP-SGD for online LDP problems with practical convergence rates.
problem Analyzing DP-SGD for online LDP problems with practical convergence rates.
method Developed a general framework for online LDP model in stochastic optimization problems, conducted non-asymptotic convergence analysis.
result Comprehensive non-asymptotic convergence analysis of the proposed estimators in finite-sample situations.
NeCPD improves online tensor decomposition using SGD with Hessian analysis and NAG.
problem Efficiently decompose multi-way tensors in online data processing.
method NeCPD solver based on SGD with Hessian analysis and NAG.
result NeCPD provides more accurate results than existing methods.
Here, we study different update rules in stochastic gradient descent (SGD) for online forecasting problems. The selection of the learning rate parameter is critical in SGD. However, it may not be feasible to tune this parameter in online learning. Therefore, it is necessary to have an update rule that is not sensitive …
New method for online statistical inference in contextual bandits using SGD.
problem Online decision-making in contextual bandits with statistical inference.
method Weighted stochastic gradient descent for adaptive data collection.
result Asymptotic normality of the parameter estimator with improved efficiency.
Study improves covariance estimation for SGD under Markovian data, matching best rates.
problem Improving covariance estimation for SGD in Markovian data settings.
method Online overlapping batch-means covariance estimator for SGD under Markovian sampling.
result Established convergence rates for covariance estimation under Markovian sampling.
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.
New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.
problem Improving SGD for robust and quantile regression with sub-quadratic convergence.
method Piecewise Lyapunov function for first-order differentiable functions.
result First geometrical convergence result for sub-quadratic SGD.
Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of work on SGD, much less is known about the statistical inferential properties of SGD-based predictions. Taking a fu…
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 i l d e O ( d P L − 1 ) ilde{O}(d P^{L-1}) i l d e O ( d P L − 1 ) samples for multi-index models. Paper develops methods for statistical inference with SGD in nonconvex optimization.
problem Statistical inference for nonconvex optimization problems.
method Proposes two online inferential procedures combining SGD and bootstrap techniques.
result Establishes error convergence rates and asymptotically valid bootstrap confidence intervals.
New method improves online covariance estimation for SGD.
problem Improving online covariance estimation for SGD.
method Proposes a de-biased covariance estimator that eliminates second-order derivatives.
result Achieves a convergence rate of n ( α − 1 ) / 2 log n n^{(α-1)/2} \sqrt{\log n} n ( α − 1 ) /2 log n , outperforming existing methods. GALA adapts learning rates online by aligning gradients, improving deep learning model performance.
problem Fine-tuning learning rates for deep learning models requires extensive grid search.
method GALA dynamically adjusts learning rates by tracking gradient alignment and local curvature.
result GALA produces a flexible, adaptive learning rate schedule that increases when gradients align.
The paper provides CI for test unfairness of group-fairness-aware classifiers trained with online SGD.
problem Ensuring fairness in machine learning models trained with stochastic gradient descent.
method Developed an online multiplier bootstrap method to estimate CI for test unfairness of DI and DM-aware linear classifiers.
result Asymptotic Central Limit Theorem holds for CI estimation of DI and DM-aware models.
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 1/k 1/ k decay rate for expected suboptimality. Proves local convergence of various online and recurrent optimization algorithms.
problem Proves local convergence of online and recurrent optimization algorithms not covered by standard stochastic gradient descent theory.
method Uses a general set of assumptions for learning dynamical systems online, adopting an 'ergodic' viewpoint.
result Local convergence results for online and recurrent optimization algorithms, including RMSProp, NoBackTrack, UORO, Adam, and RTRL.
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 q q -th moment convergence of SGD and ASGD. Improved SGD learning for single index models reduces sample complexity.
problem Learning a single index model with optimal sample complexity.
method Using smoothed loss in online SGD to reduce sample complexity.
result Online SGD with smoothed loss achieves optimal sample complexity of d k ⋆ / 2 d^{k^\star/2} d k ⋆ /2 . The paper investigates heavy-tailed behavior in offline SGD, showing it approximates power-law tails.
problem Understanding heavy-tailed behavior in offline (multi-pass) SGD with finite data.
method Proves nonasymptotic Wasserstein convergence bounds for offline SGD to online SGD.
result Offline SGD exhibits approximate power-law tails as the number of data points increases.
The paper analyzes SGD with dropout regularization in linear models, proving asymptotic properties and providing inference tools.
problem Analyzing the behavior of SGD with dropout regularization in linear models.
method Establishing geometric-moment contraction (GMC) and proving quenched central limit theorems (CLT).
result The existence of a unique stationary distribution and asymptotic normality results for SGD with dropout.
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.
SGD performs optimally on dependent data, achieving both estimation and regret.
problem Performance of SGD on temporally dependent data.
method Stochastic gradient descent with martingale-type and sequential dependence.
result SGD achieves optimal estimation and regret under various dependence structures.
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.
Preconditioned SGD accelerates convergence for ill-conditioned huge-scale matrix completion.
problem Recovering a low-rank matrix from incomplete data with high condition number.
method Preconditioned Stochastic Gradient Descent (SGD) for huge-scale online optimization.
result Preconditioned SGD converges to ε-accuracy in O(log(1/ε)) iterations, compared to O(κlog(1/ε)) for unpreconditioned SGD.
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.
A distributed system identification method for LTI systems using reverse experience replay.
problem Online system identification of LTI systems over multi-agent networks.
method DSGD-RER, a distributed variant of SGD-RER with backward updates.
result The estimation error decreases as the network size grows.
Paper studies PSGD for constrained optimization problems and its statistical properties.
problem Online inference for constrained optimization problems.
method Stochastic gradient descent with projection (PSGD) for constrained optimization.
result Limiting distribution of PSGD-based estimates under linear-equality constraints.
Online SGD achieves consistent estimation in high-dimensional non-convex inference tasks.
problem Consistent estimation in high-dimensional non-convex optimization problems.
method Online stochastic gradient descent (SGD) on non-convex losses.
result Nearly sharp thresholds for sample complexity in high-dimensional settings.
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.
We study convergence properties of Stochastic Gradient Descent (SGD) for convex objectives without assumptions on smoothness or strict convexity. We consider the question of establishing that with high probability the objective evaluated at the candidate minimizer returned by SGD is close to the minimal value of the ob…
Develops a parameter-free SGD algorithm with optimal convergence rate.
problem Optimizing parameters in stochastic convex optimization.
method A novel parameter-free algorithm for SGD with high-probability guarantees and adaptive properties.
result Achieves optimal convergence rate with only a double-logarithmic factor increase compared to known-parameter settings.
Paper introduces online tensor inference for real-time data analysis.
problem Real-time processing of high-dimensional tensor data.
method Stochastic Gradient Descent (SGD) for efficient online inference.
result Establishes non-asymptotic convergence and optimal estimation error rate.
Derives scaling limits and fluctuations for SGD in high dimensions.
problem Understanding SGD behavior in high-dimensional settings with varying noise levels.
method Interacting particle system approach, treating SGD iterates as such, with covariance structure considered.
result Precise three-step phase transition observed in SGD behavior: ballistic, diffusive, then random.
Stochastic Gradient Descent (SGD) has played a central role in machine learning. However, it requires a carefully hand-picked stepsize for fast convergence, which is notoriously tedious and time-consuming to tune. Over the last several years, a plethora of adaptive gradient-based algorithms have emerged to ameliorate t…
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.
PAGE is a simple gradient estimator for nonconvex optimization problems.
problem Nonconvex optimization problems in machine learning.
method PAGE is a probabilistic gradient estimator that uses vanilla SGD with probability and a small adjustment with probability 1-p.
result PAGE achieves optimal convergence rates for nonconvex finite-sum and online problems.
This paper introduces a novel online inference method for high-dimensional GLMs.
problem Real-time analysis of sequentially collected data in high-dimensional settings.
method Adaptive stochastic gradient descent with online debiasing for dynamic objective functions.
result Established the asymptotic normality of the Adaptive Debiased Lasso (ADL) estimator.
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.