The paper studies stochastic gradient descent with infinite variance gradients.
problem Theoretical properties of SGD with infinite variance gradients.
method Establish asymptotic behavior of SGD with infinite variance gradients.
result Asymptotic distribution of SGD is characterized as a stationary distribution of an Ornstein-Uhlenbeck process driven by a stable Lévy process.
The paper examines how SGD noise deviates from Gaussian distribution.
problem Understanding why SGD outperforms GD in neural networks.
method Analysis of SGN vectors' distribution during training.
result For large batch sizes, SGN vectors are mostly Gaussian in early phases.
Kalman Gradient Descent optimizes machine learning models by reducing variance in stochastic optimization.
problem Reducing variance in stochastic gradient descent to improve optimization performance.
method Uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent.
result Improved performance on various machine learning tasks including neural networks and black box variational inference.
Paper reduces communication in distributed machine learning.
problem Reduces burdensome communication in distributed machine learning.
method Introduces communication-censoring technique to reduce transmissions of variables.
result CSGD algorithm achieves same convergence rate as SGD but with significant communication reduction.
Paper addresses fault-tolerance in distributed machine learning with stochastic gradient descent.
problem Fault-tolerance in distributed stochastic gradient descent (D-SGD) for machine learning.
method Proposes norm-based comparative gradient elimination (CGE) to robustify D-SGD against Byzantine faulty agents.
result CGE guarantees fault-tolerance against a bounded fraction of Byzantine agents under standard stochastic assumptions.
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
SGD reduces test error by decorrelating updates.
problem Improving generalization error in machine learning models.
method Derive a formula for generalization gap change due to SGD updates, compare to GD, and show decorrelation effect.
result SGD implicitly regularizes generalization error by decorrelating updates.
Researchers analyze SGD dynamics using von Mises-Fisher distributions.
problem Understanding the dynamics of stochastic gradient descent in high-dimensional spaces.
method Geometric analysis of minibatch gradient norms and directions through von Mises-Fisher distribution.
result Directional uniformity of minibatch gradients increases over SGD iterations.
New method optimizes SDE models using continuous-time gradient descent.
problem Optimizing over the stationary distribution of SDE models.
method Continuous-time stochastic gradient descent for SDE models.
result Asymptotic convergence to the direction of steepest descent.
Stochastic NGD approximates Bayesian posterior samples near local minima.
problem Approximating Bayesian uncertainty in model parameters near local minima.
method Develops minibatch natural gradient descent (NGD) and introduces stochastic NGD to preserve Bayesian properties.
result Minibatch NGD's stationary distribution approaches a Bayesian posterior near local minima with small learning rates.
Stochastic Gradient Descent approximates Bayesian inference.
problem Approximating Bayesian posterior distributions efficiently.
method Constant SGD with parameter tuning and momentum.
result Constant SGD can approximate posterior distributions with minimized KL divergence.
Gradient descent with delayed updates converges faster with noise, even when delays are significant.
problem Analyzing convergence of gradient descent with delayed gradients and stochastic noise.
method Novel technique using generating functions for convergence analysis.
result Convergence bounds show that stochastic noise mitigates the negative effects of delays, improving performance.
Two novel algorithms improve distributed machine learning in the presence of Byzantine adversaries.
problem Improving distributed machine learning in the presence of Byzantine adversaries.
method Two novel stochastic gradient descent algorithms, ByGARS and ByGARS++, using reputation scores for gradient aggregation.
result Robust to any number of multiplicative noise Byzantine adversaries and converge for strongly convex loss functions.
Proposes variance reduction for optimizing permutation models.
problem High variance in gradient estimates for discrete latent variables.
method Control variates for the Plackett-Luce distribution.
result Optimization of black-box functions over permutations using SGD.
Deterministic GD can behave stochastically in large learning rates for multiscale functions.
problem Understanding deterministic GD's stochastic behavior in large learning rates for multiscale objectives.
method Established a sufficient condition for deterministic GD to converge to a rescaled Gibbs distribution in large learning rates for multiscale functions.
result Deterministic GD can converge to a statistical distribution in large learning rates for multiscale functions.
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
problem Optimizing functionals over probability distributions using finite particle systems.
method Virtual particle stochastic approximation, viewed as a form of stochastic gradient descent in the Wasserstein space.
result The algorithm's output converges to the optimal distribution and produces i.i.d. samples.
Paper improves SGD for Byzantine failures in distributed optimization.
problem Distributed stochastic optimization with Byzantine failures.
method Variant of SGD that tolerates up to α-fraction of Byzantine machines.
result Achieves approximate minimizers in optimal number of iterations.
Zeno improves SGD for distributed learning with faulty nodes.
problem Fault tolerance for distributed SGD with arbitrary faulty workers.
method Suspicion-based fault-tolerance mechanism with ranking-based preference.
result Proved convergence of SGD for non-convex problems under faulty scenarios.
MT-SGD samples from multiple target distributions using gradient descent.
problem Sampling from multiple unnormalized target distributions.
method Proposes MT-SGD, a flow of intermediate distributions to sample from multiple target distributions.
result Asymptotic analysis shows MT-SGD reduces to multiple-gradient descent for multi-objective optimization.
GoSGD speeds up deep learning training with gossip exchange.
problem Speeding up the training of deep learning models.
method Distributed optimization using stochastic gradient descent with gossip algorithms.
result GoSGD achieves fully asynchronous and decentralized training.
Gradient coding technique improves efficiency and accuracy in distributed machine learning.
problem Mitigating delays caused by slow nodes in distributed machine learning.
method Gradient coding via the stochastic block model.
result SBCs are efficient, accurate, and resistant to adversarial stragglers.
LASG improves communication efficiency in distributed learning.
problem Efficiently communicating gradients in distributed machine learning.
method Develops a new stochastic gradient descent approach, LASG, that predicts and selects significant communication rounds.
result Achieves communication savings by an order of magnitude in federated learning.
New method uses Chebyshev expansions to compute unbiased stochastic gradients for spectral functions.
problem Computing gradients of spectral functions is expensive and challenging.
method Combining randomized trace estimators with Chebyshev expansions for unbiased stochastic gradients.
result Developed methods for optimizing objectives involving spectral-sums with fast and stable convergence.
Stochastic gradient descent approximates Gaussian process posteriors efficiently.
problem Efficiently sampling from Gaussian process posteriors with limited computational resources.
method Developed stochastic gradient optimization objectives for sampling from Gaussian process posteriors.
result Stochastic gradient descent produces accurate predictive distributions, even in non-convergent cases.
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.
Law derived for neural networks with sparse connections.
problem Understanding the behavior of neural networks with sparse connections.
method Law of large numbers for empirical distribution of parameters derived.
result Law for neural networks with sparse connections derived.
New stochastic gradient descent with random search directions improves efficiency and convergence.
problem Efficiency and convergence of stochastic gradient descent methods.
method Developed a new class of stochastic gradient descent algorithms with random search directions.
result Established almost sure convergence and provided Lp rates of convergence. New perturbative method improves stochastic gradient descent for binary weights.
problem Improving stochastic gradient descent for binary weights.
method Perturbative expansion around the mean of the sampling distribution, Taylor-corrected estimators, variance reduction techniques.
result Perturbative correction improves convergence of stochastic variational inference.
Byrd-SAGA reduces variance to robustify SGD against Byzantine attacks.
problem Learning over networks with malicious Byzantine attacks.
method Byrd-SAGA uses geometric median for robust aggregation of corrected stochastic gradients.
result Byrd-SAGA achieves provably linear convergence to optimal solution in the presence of Byzantine workers.
Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset)…
Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of inference. In this paper, we propose a scalable distributed Bayesian matrix factorizat…
SGD improves DR by solving two-stage sampling problems.
problem Improving the learning properties of SGD for distribution regression.
method Applying SGD to two-stage sampling problems in distribution regression.
result Theoretical guarantees for SGD's performance in DR, with optimal bounds.
SGD in DLNs reveals feature learning dynamics.
problem Understanding SGD dynamics in DLNs during saddle-to-saddle training.
method Stochastic Langevin dynamics with anisotropic, state-dependent noise; one-dimensional per-mode SDEs; Boltzmann distribution approximation.
result SGD noise encodes feature learning progression but does not alter saddle-to-saddle dynamics.
DORE reduces communication costs in distributed learning by 95%.
problem High communication costs in distributed learning for large-scale models.
method DORE: Double Residual Compression Algorithm for stochastic gradient descent.
result DORE reduces communication costs by over 95%.
Convolutional linear classifiers generalize better than non-convolutional ones in structured data.
problem Understanding why gradient descent can lead to better generalization in deep learning models.
method Analyzing the generalization performance of two-layer convolutional linear classifiers with gradient descent, considering data distribution and convolutional filter size.
result Convolutional layers improve generalization in structured data compared to non-convolutional layers.
Stochastic gradient descent on manifolds improves low-rank approximation.
problem Efficiently approximate large matrices with lower rank.
method Stochastic gradient descent on a manifold.
result Algorithm outperforms Euclidean space methods on Netflix Prize data.
Noise balance theory explains SGD's behavior in neural networks.
problem Understanding SGD's navigation in neural network loss landscapes.
method Analyzes minibatch noise and loss function symmetries.
result Derives the stationary distribution of SGD for deep networks.
A new method improves stochastic gradient descent for faster and more efficient estimation.
problem Efficient and fast parametric estimation methods.
method Projected stochastic gradient descent corrected by Fisher scoring.
result The method is faster and more efficient than traditional methods.
New biased compression methods lead to faster convergence in distributed learning.
problem Improving convergence rates in distributed learning with biased compression.
method Study of three classes of biased compression operators in distributed learning.
result Biased compressors can lead to linear convergence rates in both single node and distributed settings.
FedAc accelerates Federated Averaging for distributed optimization.
problem Efficiently optimizing distributed machine learning models.
method Federated Accelerated Stochastic Gradient Descent (FedAc) using a potential-based perturbed iterate analysis.
result FedAc achieves faster convergence and lower communication costs than previous methods.
Efficient variational inference for probabilistic models using importance sampling.
problem Efficiently approximating posterior distributions in probabilistic models.
method Develops importance sampled stochastic gradient descent for variational inference.
result Importance sampled stochastic gradient descent outperforms standard methods for various models.
The paper analyzes how gradient descent learns convolutional filters for non-Gaussian inputs.
problem Learning convolutional filters with ReLU for non-Gaussian input distributions.
method Analysis of gradient descent convergence for ReLU activation with polynomial time complexity.
result Gradient descent can learn convolutional filters in polynomial time, with convergence rate dependent on input distribution smoothness and patch similarity.
A new decentralized method solves minimax problems with reduced communication and sample complexity.
problem Solving minimax optimization problems in a distributed setting.
method Decentralized stochastic gradient descent ascent with variance reduction.
result Achieved optimal sample and communication complexities for nonconvex-strongly-concave problems.
New distributed algorithm for gradient descent converges linearly in the interpolation limit.
problem Analyzing convergence of stochastic gradient descent in the interpolation limit of high-dimensional data fitting.
method Introduced a distributed gradient descent algorithm for the penalized distributed loss function, showing linear convergence rate.
result Distributed SGD algorithm converges linearly with rate 1-η/nλ_min(H), where λ_min(H) is the smallest nonzero eigenvalue of the Hessian.
Gradient descent with random weights in linear regression analyzed for various noise types.
problem Analyzing the impact of random noise on gradient descent in linear regression.
method Gradient descent with randomly weighted data points, various weighting distributions, geometric moment contraction.
result Characterization of implicit regularization and non-asymptotic convergence bounds.
Stochastic gradient descent converges to universal limits in high dimensions.
problem Statistical tasks in high dimensions with specific data projections.
method Stochastic gradient descent applied to mixture distributions, proving universality of limits.
result The ODE limits are universal for mixtures of arbitrary product distributions.
New method reduces communication costs in distributed nonconvex optimization.
problem Large communication costs between central server and local workers in distributed learning.
method Communication-compressed AMSGrad for distributed nonconvex optimization.
result Converges to first-order stationary point with same iteration complexity as vanilla AMSGrad.
New adaptive step-size method for convex optimization without tuning.
problem Optimizing convex functions efficiently with stochastic gradients.
method Adapted Adaptive Gradient Descent Without Descent to stochastic setting.
result Stochastic gradient descent converges under various assumptions.