Exact minibatch MH method improves scalability for large datasets.
problem Inexactness in minibatch MH methods causes inference errors.
method TunaMH proposes an exact minibatch MH method with a tunable batch size.
result TunaMH is asymptotically optimal in terms of batch size.
Adaptive batch sizes improve local gradient methods in distributed training.
problem Communication bottlenecks in distributed deep learning.
method Adaptive batch size strategies for local gradient methods.
result Adaptive batch sizes reduce minibatch gradient variance and improve training efficiency.
It is well known that, for most datasets, the use of large-size minibatches for Stochastic Gradient Descent (SGD) typically leads to slow convergence and poor generalization. On the other hand, large minibatches are of great practical interest as they allow for a better exploitation of modern GPUs. Previous literature …
Recent work has argued that stochastic gradient descent can approximate the Bayesian uncertainty in model parameters near local minima. In this work we develop a similar correspondence for minibatch natural gradient descent (NGD). We prove that for sufficiently small learning rates, if the model predictions on the trai…
We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of Metropolis-Hastings tests yield variable data consumed per sample, with only constant factor reductions versus using the full dataset for each sample. Here we present…
Unified analysis of stochastic gradient methods for convex and smooth optimization.
problem Minimizing composite convex and smooth functions.
method Unified convergence analysis of various stochastic gradient methods.
result Unified convergence rates for a variety of methods including proximal SGD, variance reduced methods, quantization, and coordinate descent.
Develops minibatch stochastic proximal gradient for large-scale learning models.
problem Finding optimal predictors with complex regularizers in large-scale learning models.
method Minibatch variants of stochastic proximal gradient algorithm for composite objective functions.
result Minibatch size N after O(Nε1) iterations achieves ε−suboptimality in expected quadratic distance. Paper proves minibatch SGD for GP inference converges and improves generalization.
problem Theoretical understanding and practical use of SGD for correlated samples in Gaussian process inference.
method Proves minibatch SGD converges to a critical point with rate O(1/K) for K iterations, under certain kernel conditions.
result Minibatch SGD for GP inference improves generalization and reduces computational burden.
SGD converges to global minimum for structured non-convex functions.
problem Optimizing non-convex functions using SGD with slow convergence rates.
method Convergence theorems for SGD on structured non-convex functions, including Quasar and PL conditions.
result SGD converges to global minimum for specific non-convex functions under certain conditions.
This work improves SGD minibatch sampling using determinantal point processes based on orthogonal polynomials.
problem Improving variance reduction in stochastic gradient descent (SGD) for large datasets.
method Orthogonal polynomial-based determinantal point processes for sampling minibatches in SGD.
result DPP minibatches lead to a smaller mean square approximation error than uniform minibatches.
New method shows stochastic momentum can converge quickly on optimization problems.
problem Improving convergence of stochastic optimization methods.
method Stochastic heavy ball momentum with minibatching.
result Stochastic heavy ball momentum retains fast linear rate on quadratic problems.
Anytime MiniBatch speeds up online distributed optimization by handling slow nodes.
problem Mitigating the impact of slow nodes (stragglers) in distributed optimization.
method Proposes an online distributed optimization method that averages minibatch gradients via consensus rounds.
result Prevents stragglers from slowing progress without wasting work.
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.
Paper proposes a method to estimate variance reduction in DNN training using importance sampling.
problem Challenges in assessing variance reduction during DNN training using importance sampling.
method Proposes a method for estimating variance reduction using minibatches sampled under importance sampling.
result Demonstrates consistent reduction in variance, improved training efficiency, and enhanced model accuracy.
New algorithms accelerate model-based optimization for stochastic problems.
problem Optimizing model-based stochastic optimization problems efficiently.
method Proposed new model-based algorithms with acceleration and minibatch techniques.
result Non-asymptotic convergence guarantees with linear speedup in minibatch size.
We present an approach towards convex optimization that relies on a novel scheme which converts online adaptive algorithms into offline methods. In the offline optimization setting, our derived methods are shown to obtain favourable adaptive guarantees which depend on the harmonic sum of the queried gradients. We furth…
SGLRW improves robustness of stochastic gradient MCMC methods.
problem Sensitivity to minibatch size and gradient noise in stochastic-gradient MCMC methods.
method Proposes Stochastic Gradient Lattice Random Walk (SGLRW) with lattice-based discretization.
result SGLRW remains stable in regimes where SGLD fails, including heavy-tailed gradient noise.
FedProx algorithm improved for non-smooth and heterogeneous data.
problem Theoretical understanding of FedProx for non-convex federated optimization.
method Local dissimilarity invariant convergence theory through algorithmic stability.
result Convergence guarantees for non-smooth FL problems and minibatch size.
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.
Stochastic gradient Markov Chain Monte Carlo (SG-MCMC) has been developed as a flexible family of scalable Bayesian sampling algorithms. However, there has been little theoretical analysis of the impact of minibatch size to the algorithm's convergence rate. In this paper, we prove that under a limited computational bud…
Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale to large graphical models by reducing its computational cost. In this paper, we p…
New algorithm reduces FL sample and communication costs.
problem Optimizing FL for minimal samples and rounds.
method Stochastic two-sided momentum algorithm.
result Achieves near-optimal sample and communication complexities.
EigenGame improves eigendecomposition by offering unbiased updates for larger datasets.
problem Minibatch bias in EigenGame limits convergence and parallelism.
method Proposed unbiased stochastic update for EigenGame.
result Asymptotic equivalence to EigenGame, greater parallelism, and improved performance.
We study local SGD (also known as parallel SGD and federated averaging), a natural and frequently used stochastic distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD.…
We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise th…
While stochastic gradient descent (SGD) is one of the major workhorses in machine learning, the learning properties of many practically used variants are poorly understood. In this paper, we consider least squares learning in a nonparametric setting and contribute to filling this gap by focusing on the effect and inter…
Study on gradient complexity of private optimization with private oracles.
problem Analyzing the efficiency of differentially private optimization algorithms.
method Lower bounds on the number of first-order oracle queries for private optimization.
result Lower bounds on the number of queries for private optimization algorithms, showing a dimension-dependent runtime penalty.
Noise enhancement improves generalization in training.
problem Improving generalization in training with controlled noise.
method Noise enhancement method to control SGD noise without changing learning rate or minibatch size.
result Noise enhancement improves generalization for real datasets.
New sampling technique improves KGC model performance.
problem Ignoring entity neighbors in minibatches affects KGC model training.
method Random-walk based minibatch sampling.
result Proposed method achieves state-of-the-art performance on DB100K.
New method improves convergence of SPP for convex optimization problems.
problem Stochastic optimization and robustness to SGD.
method Minibatch Stochastic Proximal Point (M-SPP) method with stability analysis.
result M-SPP achieves faster convergence rates under smoothness and quadratic growth conditions.
This paper analyzes minibatch optimal transport distances and their applications.
problem Optimal transport distances are complex and impractical for large datasets.
method Extended analysis of minibatch optimal transport distances, focusing on various kernels and debiased functions.
result Minibatch optimal transport distances are unbiased estimators and have statistical and optimisation properties.
New approach speeds up optimization with repeated gradient steps on same batch.
problem Performance bottlenecks in massive parallel pipelines with large batch sizes.
method Data echoing, taking repeated gradient steps on the same batch.
result Data echoing affords speedups on curvature-dominated part of convergence rate.
In this paper, we design and analyze a new zeroth-order online algorithm, namely, the zeroth-order online alternating direction method of multipliers (ZOO-ADMM), which enjoys dual advantages of being gradient-free operation and employing the ADMM to accommodate complex structured regularizers. Compared to the first-ord…
Improved algorithm reduces stochastic gradient complexity for large-scale learning problems.
problem High stochastic gradient complexity for large-scale learning problems.
method Hybrid Stochastic-Deterministic Minibatch Proximal Gradient (HSDMPG) algorithm.
result Achieves nearly optimal generalization in less than a single pass over data.
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…
The Lookahead optimizer improves SGD's performance and generalization without restrictive assumptions.
problem Improving the generalization of SGD with Lookahead.
method A rigorous stability and generalization analysis of the Lookahead optimizer with minibatch SGD, leveraging on-average model stability.
result Derives generalization bounds for convex and strongly convex problems without the restrictive Lipschitzness assumption, demonstrating a linear speedup with batch size.
Unbalanced minibatch Optimal Transport improves domain adaptation performance.
problem Optimal transport distances are computationally expensive for large datasets.
method Use unbalanced minibatch Optimal Transport to estimate distances over subsets of data.
result Unbalanced Optimal Transport leads to better domain adaptation results.
Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better char…
New types of machine learning hardware in development and entering the market hold the promise of revolutionizing deep learning in a manner as profound as GPUs. However, existing software frameworks and training algorithms for deep learning have yet to evolve to fully leverage the capability of the new wave of silicon.…
New DPP kernels improve minibatch efficiency for large datasets.
problem Efficiently generating minibatches from large datasets.
method Wavelet-based DPPs and novel discrete conversion methods.
result Improved minibatch efficiency with low-rank decompositions.
Machine learning, especially deep neural networks, has been rapidly developed in fields including computer vision, speech recognition and reinforcement learning. Although Mini-batch SGD is one of the most popular stochastic optimization methods in training deep networks, it shows a slow convergence rate due to the larg…
Improved convergence analysis for decentralized non-convex optimization.
problem Minimizing a sum of smooth non-convex functions over a network.
method Gradient tracking in decentralized stochastic gradient descent (GT-DSGD).
result GT-DSGD achieves network-independent performances matching centralized SGD under certain conditions.
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.
New minibatching strategy reduces stochastic gradient bias in optimisation.
problem Reducing bias in stochastic gradient descent.
method Symmetric Minibatching Strategy combined with momentum.
result Reduced stochastic gradient bias from O(h2) to O(h4). Minibatching is a very well studied and highly popular technique in supervised learning, used by practitioners due to its ability to accelerate training through better utilization of parallel processing power and reduction of stochastic variance. Another popular technique is importance sampling -- a strategy for prefer…
DReg boosts large-batch SGD's generalization and convergence.
problem Large-batch SGD struggles with generalization in deep learning.
method DReg replicates a layer to encourage parameter diversity.
result DReg improves generalization and convergence with large-batch SGD.
Stochastic Gradient Descent (SGD) is a popular optimization method which has been applied to many important machine learning tasks such as Support Vector Machines and Deep Neural Networks. In order to parallelize SGD, minibatch training is often employed. The standard approach is to uniformly sample a minibatch at each…
New method reduces discrete flow transitions, improving perplexity estimation.
problem Stochasticity in discrete paths makes rectification strategies ineffective.
method Dynamic-optimal-transport-like minimization objective with minibatch strategies.
result 32 times reduction in transitions for same perplexity.