We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena \latestEdits{from our theoretical results:} (1) The importance of combining iterate averag…
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33 results for “Iterate-Averaging”
Improved SEG method converges to Nash equilibrium in bilinear games.
problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.
Improving optimization for iterate-averaged language models
problem How to optimize the averaged model returned by Language Model pipelines
method Formulating optimizer design as an optimal-control problem
result Proven convergence rate and strict improvement in squared error
PACE optimizes training for averaged language models, improving performance.
problem How to optimize training for averaged language model iterates.
method Formulated as an optimal-control problem, solved for minimizing error of the average with a penalty on intervention size.
result PACE improves the limiting squared error of the iterate-average estimator by an arbitrarily large factor on some instances.
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.
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The…
The paper estimates common mean of entangled Gaussians with bounded variances.
problem Estimating common mean of entangled Gaussians with bounded variances.
method Iteratively averaging truncated samples.
result Achieves error $O \left(\frac{\sqrt{n\ln n}}{m}
ight)$ with high probability when .
We propose and analyze a variant of the classic Polyak-Ruppert averaging scheme, broadly used in stochastic gradient methods. Rather than a uniform average of the iterates, we consider a weighted average, with weights decaying in a geometric fashion. In the context of linear least squares regression, we show that this …
Improved DP-SGD for variational inference reduces noise and variance.
problem Poor convergence and high variance in variational parameter outputs due to gradient noise in DP-SGD.
method Introduced aligned gradients and iterate averaging to reduce DP-induced noise, and noise-aware posteriors.
result Less noisy gradient estimator and improved parameter estimates for variational inference.
New methods improve temporal difference learning for policy evaluation in Markov decision processes.
problem Improving temporal difference learning for policy evaluation in Markov decision processes.
method Introduced variance-reduced forms of stochastic approximation to achieve non-asymptotic, instance-dependent optimality.
result Temporal difference learning is strictly suboptimal, but variance-reduced forms achieve optimality up to logarithmic factors.
We provide non-asymptotic bounds for the well-known temporal difference learning algorithm TD(0) with linear function approximators. These include high-probability bounds as well as bounds in expectation. Our analysis suggests that a step-size inversely proportional to the number of iterations cannot guarantee optimal …
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.
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.
New method schedules learning rate without stopping time, outperforming existing methods.
problem Learning rate schedules that require stopping time are outperformed.
method Schedule-Free approach that avoids stopping time and introduces no additional hyper-parameters.
result Exhibits state-of-the-art performance across various problems.
We give a construction of a universal average of Lie algebra elements whose exponentiation gives (when there is an associated Lie group) a totally symmetric geometric mean of Lie group elements (sufficiently closed to the identity) with the property that in an action of the group on a space for which elements a…
We analyze SGAs for statistical inference via asymptotics, improving tuning methods.
problem Improper tuning of SGAs for optimization and sampling.
method Characterize large-sample asymptotics of SGAs via step-size and sample-size scaling limits.
result Iterate averaging with large step size is robust and asymptotically has covariance proportional to MLE's.
New streaming methods improve convergence rates for optimization problems.
problem Optimizing large-scale, sequential data problems.
method Time-varying mini-batches and Polyak-Ruppert averaging for gradient-based algorithms.
result Time-varying mini-batches and averaging achieve optimal convergence and variance reduction.
New algorithm improves distributed SGD with random sparsification for better convergence and generalization.
problem Communication bottleneck in distributed deep learning.
method Proposes detached error feedback (DEF) algorithm to improve convergence and generalization of communication-efficient distributed SGD.
result Shows better convergence and generalization bounds than existing methods.
Accurate Large-sample Uncertainty Quantification using Stochastic Gradient Markov Chain Monte Carlocs.LG
New method improves uncertainty quantification for large batch sizes and misspecified models.
problem Challenges in tuning algorithms for accurate uncertainty quantification in large batch sizes and misspecified models.
method Proposes new discrete-time approximations to SGD and SGLD, proving error bounds for practical tuning.
result Quantitative, non-asymptotic error bounds for accurate predictions of covariance and autocorrelation time.
BEMA reduces bias in EMA, leading to faster convergence and better performance.
problem Stochasticity in language model fine-tuning destabilizes training.
method Bias-Corrected Exponential Moving Average (BEMA) augmentation of EMA.
result BEMA leads to significantly improved convergence rates and final performance.
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.
Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. In this paper, we study one-step and iterative weighted parameter averaging in s…
Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most first-order methods only guarantee an ergodic convergence rate, that is, the uniform…
Faster algorithms for solving multichain MDPs under average-reward criterion.
problem Navigating towards the best connected component in multichain MDPs.
method Developed algorithms to better solve the navigational subproblem, achieving faster convergence rates.
result Improved rates of convergence and sharper complexity measures for multichain MDPs.
Stochastic Gradient Descent (SGD) is a central tool in machine learning. We prove that SGD converges to zero loss, even with a fixed (non-vanishing) learning rate - in the special case of homogeneous linear classifiers with smooth monotone loss functions, optimized on linearly separable data. Previous works assumed eit…
GPA improves LLM training speed by 8.71% for Llama-160M models.
problem Training Large Language Models (LLMs) with high memory overhead and slow convergence.
method Generalized Primal Averaging (GPA) extends Nesterov's method to eliminate memory-intensive two-loop structure.
result GPA achieves up to 10.13% speedup over AdamW in training Llama-1B model.
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).
Derives error bounds for stochastic iterative algorithms using Stein's method.
problem Bounding errors in stochastic iterative algorithms like SGD and SGLD.
method Uses infinite-dimensional Stein's method of exchangeable pairs to derive functional approximation error bounds.
result Establishes non-asymptotic error bounds for algorithm sample paths and variance of iterate averages.
Flatness is a False Friendstat.ML
New findings challenge the use of flatness measures in neural networks.
problem The validity of flatness measures in assessing generalization in neural networks.
method Analysis of Hessian-based flatness norms and their relation to generalization.
result Solutions with large weights and low loss are often sharper than expected, contradicting flatness measures.
The choice of how to retain information about past gradients dramatically affects the convergence properties of state-of-the-art stochastic optimization methods, such as Heavy-ball, Nesterov's momentum, RMSprop and Adam. Building on this observation, we use stochastic differential equations (SDEs) to explicitly study t…
Paper analyzes SGD in kernel regression, showing it outperforms offline methods.
problem Performance of SGD in kernel regression compared to offline methods.
method Analyzes Stochastic Gradient Descent (SGD) in kernel regression under misspecified models.
result SGD achieves min-max optimal rates up to constants, avoiding saturation.
We consider -dimensional linear stochastic approximation algorithms (LSAs) with a constant step-size and the so called Polyak-Ruppert (PR) averaging of iterates. LSAs are widely applied in machine learning and reinforcement learning (RL), where the aim is to compute an appropriate (that is a…
Minimax optimal convergence rates for classes of stochastic convex optimization problems are well characterized, where the majority of results utilize iterate averaged stochastic gradient descent (SGD) with polynomially decaying step sizes. In contrast, SGD's final iterate behavior has received much less attention desp…