We analyze a fast incremental aggregated gradient method for optimizing nonconvex problems of the form . Specifically, we analyze the SAGA algorithm within an Incremental First-order Oracle framework, and show that it converges to a stationary point provably faster than both gradient descent and s…
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48 results for “Fast Gradient Method”
Stochastic gradient method converges as fast as deterministic for overparametrized models.
problem Convergence rate of stochastic gradient methods in overparametrized models.
method Proposes a regularity condition enabling fast convergence of SGD.
result Stochastic gradient method achieves the same convergence rate as deterministic gradient method.
Natural-gradient methods enable fast and simple algorithms for variational inference, but due to computational difficulties, their use is mostly limited to \emph{minimal} exponential-family (EF) approximations. In this paper, we extend their application to estimate \emph{structured} approximations such as mixtures of E…
Stochastic gradient descent~(SGD) and its variants have become more and more popular in machine learning due to their efficiency and effectiveness. To handle large-scale problems, researchers have recently proposed several parallel SGD methods for multicore systems. However, existing parallel SGD methods cannot achieve…
A new method uses natural gradients for efficient distribution optimization.
problem Challenges in computing natural gradients for many distributions.
method Reframe optimization as a surrogate distribution with easy natural gradient computation.
result Expands set of distributions efficiently targetable with natural gradients.
Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD) with momentum in training deep neural networks. This leaves how to close the gene…
A fast method for decentralized non-convex optimization over networks.
problem Decentralized non-convex optimization problems over a network of nodes.
method GT-SAGA, a randomized incremental gradient method that evaluates one component gradient per node per iteration.
result GT-SAGA achieves almost sure and mean-squared convergence to a first-order stationary point for general smooth non-convex problems.
Quantized Variational Inference improves ELBO optimization with fast convergence.
problem Maximizing Evidence Lower Bound (ELBO) for variational inference.
method Optimal Voronoi Tesselation for variance-free gradients, Richardson extrapolation for asymptotic improvement.
result Quantized Variational Inference leads to fast convergence with comparable computational cost.
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating Bayesian inference as an optimization problem and solving it using gradient-based op…
This study explains why approximate NGD works well in wide neural networks.
problem Understanding why NGD with approximate Fisher information converges fast in wide neural networks.
method Analyzing asymptotic training dynamics in function space via the neural tangent kernel.
result NGD with approximate Fisher information achieves the same fast convergence as exact NGD under specific conditions.
PPGD solves nonconvex nonsmooth optimization problems without KL property.
problem Nonconvex and nonsmooth optimization problems in statistics and machine learning.
method Projective Proximal Gradient Descent (PPGD) for solving a class of nonconvex and nonsmooth problems.
result PPGD achieves a fast convergence rate of O(1/k^2) for k ≥ k_0.
Gradient-free method improves predictive accuracy for probabilistic models.
problem Balancing computational efficiency and robust predictive performance in deep learning.
method CAVI-CMN, a gradient-free variational method for conditional mixture networks.
result CAVI-CMN achieves competitive and often superior predictive accuracy compared to MLE with backpropagation.
SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectivescs.LG
In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG and SVRG, with better theoretical convergence rates, and has support for compos…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem is very limited. For example, it is not known whether the proximal stochastic gra…
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…
Paper introduces a new gradient statistic to improve deep learning convergence.
problem Fluctuation effect of gradient updates between iterations.
method Introduces an unbiased stratified statistic \(\bar{G}_{mst}\) and a new algorithm MSSG.
result MSSG algorithm outperforms other sgd-like algorithms in training deep models.
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.
The alternating direction method of multipliers (ADMM) is a powerful optimization solver in machine learning. Recently, stochastic ADMM has been integrated with variance reduction methods for stochastic gradient, leading to SAG-ADMM and SDCA-ADMM that have fast convergence rates and low iteration complexities. However,…
A1GM method improves efficiency in reconstructing missing data using KL divergence.
problem Efficiently reconstructing missing data in matrices.
method Fast non-gradient-based rank-1 NMF using KL divergence.
result A1GM outperforms gradient methods in efficiency with competitive reconstruction errors.
A fast method for training linear classifiers maximizes margins.
problem Training linear classifiers with maximum margins.
method Momentum-based gradient method derived from convex dual with Nesterov acceleration.
result Exponentially faster convergence rate compared to standard methods.
The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.
problem Gradient estimates for porous medium and fast diffusion equations on metric measure spaces.
method Derives Li-Yau and Souplet-Zhang type gradient estimates for the given equations.
result Gradient estimates for the equations on complete noncompact metric measure spaces with compact boundary.
Efficient momentum-based methods for reinforcement learning with improved sample complexity.
problem Efficient reinforcement learning algorithms for non-concave performance functions.
method Adaptive momentum-based policy gradient methods using variance reduction and importance sampling techniques.
result Both IS-MBPG and HA-MBPG reach the best known sample complexity of for finding an -stationary point.
DIP-FAT improves adversarial training by diversifying perturbations.
problem Adversarial examples fool deep neural networks, leading to overfitting and poor performance.
method DIP-FAT uses random directions to diversify perturbations in adversarial training.
result DIP-FAT reduces overfitting and improves clean data accuracy.
Momentum based stochastic gradient methods such as heavy ball (HB) and Nesterov's accelerated gradient descent (NAG) method are widely used in practice for training deep networks and other supervised learning models, as they often provide significant improvements over stochastic gradient descent (SGD). Rigorously speak…
Improved VI method for deep mixed models in finance.
problem Inaccurate and slow variational inference in high dimensions.
method Natural gradient hybrid VI method targeting joint posterior.
result Natural gradient method is faster and more accurate than existing methods.
High sensitivity of neural architecture search (NAS) methods against their input such as step-size (i.e., learning rate) and search space prevents practitioners from applying them out-of-the-box to their own problems, albeit its purpose is to automate a part of tuning process. Aiming at a fast, robust, and widely-appli…
A fast method for discrete OT with group-sparse regularization for class label preservation.
problem Efficiently measuring the distance between two discrete distributions with class labels.
method Fast discrete OT with group-sparse regularizers using gradient-based algorithms.
result Up to 8.6 times faster than original method without degrading accuracy.
Fast calibration of the LIBOR Market Model with Stochastic Volatility based on analytical gradientmath.OC
Proposes efficient calibration method for LIBOR Market Model with stochastic volatility.
problem Calibrating LIBOR Market Model with stochastic volatility.
method Derives analytical gradient of swaptions prices for DDSVLMM and uses it for gradient-based optimization.
result Analytical gradient-based calibration is highly competitive and efficient for DDSVLMM.
A faster method for optimizing DNA and protein sequences using machine learning.
problem Designing DNA and protein sequences with improved function.
method Activation maximization with a straight-through approximation and adaptive entropy variable.
result Fast SeqProp achieves up to 100-fold faster convergence and improved fitness optima.
We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex prob…
We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing …
In this paper, we will show an unprecedented method to accelerate training and improve performance, which called random gradient (RG). This method can be easier to the training of any model without extra calculation cost, we use Image classification, Semantic segmentation, and GANs to confirm this method can improve sp…
AdaBelief optimizes deep learning models with faster convergence and better stability.
problem Combining fast convergence and stability in deep learning models.
method Adapts stepsize based on the belief in observed gradients using exponential moving average (EMA) of noisy gradients.
result AdaBelief outperforms other methods in image classification and GAN training, achieving comparable accuracy to SGD on ImageNet.
Accelerated gradient method's stability deteriorates exponentially with steps.
problem Algorithmic stability of Nesterov's accelerated gradient method.
method Analysis of two notions of algorithmic stability for Nesterov's accelerated gradient method.
result Stability of Nesterov's accelerated method deteriorates exponentially with the number of gradient steps.
We consider gradient estimates to positive solutions of porous medium equations and fast diffusion equations: associated with the Witten Laplacian on Riemannian manifolds. Under the assumption that the -dimensional Bakry-Emery Ricci curvature is bounded from below, we obtain gradient estimates which…
The development of machine learning is promoting the search for fast and stable minimization algorithms. To this end, we suggest a change in the current gradient descent methods that should speed up the motion in flat regions and slow it down in steep directions of the function to minimize. It is based on a "power grad…
This paper analyzes adversarial attacks methods and their effectiveness.
problem Understanding the effectiveness and theoretical properties of adversarial attacks.
method Comparative and formal analysis of loss functions of three adversarial attack methods.
result The Iterative Fast Gradient Sign attack is the slowest in creating adversarial examples.
Paper proposes a new method to detect convergence in SGD.
problem Detecting the transition from fast progress to oscillation in SGD.
method Analyzes Pflug's test and proposes a novel statistical procedure.
result The novel procedure accurately detects stationarity in SGD.
Entropy-regularized NPG methods converge linearly in discounted MDPs.
problem Theoretical limitations of NPG methods in reinforcement learning.
method Entropy regularization in conjunction with NPG methods for discounted MDPs.
result Entropy-regularized NPG methods converge linearly in discounted MDPs.
A new method computes gradients without backpropagation.
problem Optimization of machine learning models.
method Forward mode automatic differentiation to compute gradients.
result Forward gradient is an unbiased estimate of the gradient, eliminating the need for backpropagation.
Paper proposes a boosting method with fast learning rates and early stopping.
problem Missing theoretical guarantees for boosting methods in binary classification.
method Fully-corrective gradient boosting with squared hinge loss and ADMM algorithm.
result Derives fast learning rates of and .
Asynchronous computation and gradient compression have emerged as two key techniques for achieving scalability in distributed optimization for large-scale machine learning. This paper presents a unified analysis framework for distributed gradient methods operating with staled and compressed gradients. Non-asymptotic bo…
Fast Stochastic Variance Reduced Gradient Method with Momentum Acceleration for Machine Learningcs.LG
Recently, research on accelerated stochastic gradient descent methods (e.g., SVRG) has made exciting progress (e.g., linear convergence for strongly convex problems). However, the best-known methods (e.g., Katyusha) requires at least two auxiliary variables and two momentum parameters. In this paper, we propose a fast …
When applied to training deep neural networks, stochastic gradient descent (SGD) often incurs steady progression phases, interrupted by catastrophic episodes in which loss and gradient norm explode. A possible mitigation of such events is to slow down the learning process. This paper presents a novel approach to contro…
A new method reduces adversarial training time without overfitting.
problem Catastrophic overfitting in single-step adversarial training.
method FGSMPR: FGSM with PGD Regularization.
result Reduces the gap to multi-step adversarial training.
Paper improves a method for fast global and local convergence in optimization.
problem Slow global convergence in optimization methods with noisy Hessian estimates.
method Stochastic Newton Proximal Extragradient method using HPE framework.
result Faster global linear rate and superlinear convergence in fewer iterations.
New method prevents adversarial training failure in deep networks.
problem Adversarial training failure in deep networks.
method GradAlign method to prevent catastrophic overfitting.
result GradAlign prevents adversarial training failure in deep networks.
We construct exhaustion and cut-off functions with controlled gradient and Laplacian on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the distance from a fixed reference point, without any assumptions on the topology or the injectivity radius. Along the way we prove…