New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
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48 results for “Gradient methods”
Accelerates Riemannian gradient methods with extrapolation.
problem Optimizing functions on manifolds efficiently.
method Extrapolating iterates in Riemannian gradient descent.
result Achieves optimal convergence rate and computational advantage.
Proposes a new adaptive gradient method based on gradient differences.
problem Manual tuning of stepsize in vanilla gradient methods.
method Adaptation driven by cumulative squared norms of gradient differences.
result More robust than AdaGrad in various settings.
Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in machine learning for massive data sets (big data). In particular, stochastic gradien…
Adaptive methods improve gradient descent and proximal gradient for convex optimization.
problem Improving efficiency of gradient descent and proximal gradient methods.
method Adaptive versions of GD and ProxGD using local curvature information.
result Proved convergence with local Lipschitz gradient assumptions.
Communication-Efficient Adaptive Batch Size Strategies for Distributed Local Gradient Methodsstat.ML
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.
Proposes log density gradient to improve reinforcement learning sample complexity.
problem Residual error in gradient estimation in policy gradient methods.
method Log density gradient method to correct residual error, using state-action discounted distributional formulation.
result Min-max optimization method to approximate log density gradient with on-policy samples, achieving sample complexity of .
Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence analysis for a general class of adaptive gradient methods including AMSGrad, RMSPr…
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
Gravilon improves gradient descent for neural networks.
problem Improving efficiency and accuracy of gradient descent methods.
method Uses geometric modification of gradient step lengths.
result Promising experimental results on MNIST classification.
Improved complexity for machine learning optimization methods.
problem Optimizing over-parametrized models in machine learning.
method Stochastic conditional gradient methods with interpolation-like conditions.
result Improved oracle complexities for finding optimal solutions.
A method for estimating the median of gradients in stochastic optimization.
problem Robust gradient estimation in stochastic optimization for various applications.
method Stochastic Proximal Point Method for median gradient estimation.
result The proposed method can converge even under heavy-tailed, state-dependent noise.
COMP-AMS optimizes distributed training with compressed gradients, achieving similar accuracy with less communication.
problem Efficiently training large-scale models in distributed environments with reduced communication costs.
method Distributed optimization framework using gradient averaging and adaptive AMSGrad, with gradient compression and error feedback.
result COMP-AMS achieves the same convergence rate and linear speedup as standard AMSGrad with less communication.
Clip21 improves convergence of gradient-clipped methods in DP settings.
problem Gradient clipping introduces bias in distributed training, causing convergence issues.
method Clip21 designs an error feedback mechanism to mitigate bias in gradient-clipped methods.
result Clip21 converges at the same rate as distributed gradient descent, improving from previous $\mathcal{O}\left(\frac{1}{\sqrt{K}}
ight)$ to $\mathcal{O}\left(\frac{1}{K}
ight)$.
Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradientscs.LG
New framework improves variational inference with Markov chain methods.
problem Challenges of minimizing KL divergence with stochastic gradient descent.
method Markov chain score ascent (MCSA) methods, including parallel MCSA (pMCSA).
result Improved theoretical and empirical performance of MCSA methods.
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole objective function is strongly convex. Such problems often arise in machine lea…
Researchers compare different gradient methods for ridge regression, finding conjugate gradients have similar performance.
problem Comparing statistical properties of different gradient methods in ridge regression.
method Explicit non-standard error decomposition to bound prediction error of conjugate gradient iterates.
result Conjugate gradient iterates share optimality properties with gradient flow and ridge regression up to a constant factor.
DBQPG improves policy gradient estimation with fewer samples.
problem Accurate policy gradient estimation with limited samples.
method Deep Bayesian Quadrature Policy Gradient (DBQPG).
result DBQPG provides more accurate and less variable gradient estimates.
This paper proves AdaGrad and Adam converge linearly under PL inequality.
problem Understanding the convergence of adaptive gradient methods.
method Unified approach proving AdaGrad and Adam converge linearly under PL inequality.
result AdaGrad and Adam converge linearly when the cost function is smooth and satisfies PL inequality.
A new method speeds up deep neural network training.
problem Nonconvex optimization in deep neural networks.
method Scaled conjugate gradient method for nonconvex optimization.
result The method converges faster and achieves lower scores in practical applications.
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.
The policy gradient approach is a flexible and powerful reinforcement learning method particularly for problems with continuous actions such as robot control. A common challenge in this scenario is how to reduce the variance of policy gradient estimates for reliable policy updates. In this paper, we combine the followi…
Proposes VSGD optimizer combining probabilistic and gradient-based methods.
problem Uncertainty modeling in deep neural networks.
method Combines probabilistic and gradient-based approaches using SVI.
result VSGD outperforms Adam and SGD on image classification tasks.
In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The sto…
Combines Integrated Gradients and PatternAttribution into PGIG, outperforming alternatives.
problem Improving neural network explainability methods.
method Combines Integrated Gradients and PatternAttribution into Pattern-Guided Integrated Gradients (PGIG).
result PGIG outperforms other explainability methods in a large-scale image degradation experiment.
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…
A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rath…
Recent advances in policy gradient methods and deep learning have demonstrated their applicability for complex reinforcement learning problems. However, the variance of the performance gradient estimates obtained from the simulation is often excessive, leading to poor sample efficiency. In this paper, we apply the stoc…
Gradient methods avoid overfitting on separable data.
problem Overfitting on separable data with gradient methods.
method Gradient methods (flow, descent, SGD) on separable data.
result Gradient methods asymptotically do not overfit on separable data.
In this paper we study the problem of minimizing the average of a large number () of smooth convex loss functions. We propose a new method, S2GD (Semi-Stochastic Gradient Descent), which runs for one or several epochs in each of which a single full gradient and a random number of stochastic gradients is computed, fo…
New method for natural policy gradients converges linearly.
problem Improving natural policy gradient methods for better convergence.
method Fisher-Rao gradient flow applied to state-action distributions.
result Linear convergence rate with geometry-dependent factor.
We apply stochastic average gradient (SAG) algorithms for training conditional random fields (CRFs). We describe a practical implementation that uses structure in the CRF gradient to reduce the memory requirement of this linearly-convergent stochastic gradient method, propose a non-uniform sampling scheme that substant…
In this paper, we provide an overview of first-order and second-order variants of the gradient descent method that are commonly used in machine learning. We propose a general framework in which 6 of these variants can be interpreted as different instances of the same approach. They are the vanilla gradient descent, the…
We propose a variance reduction framework for variational inference using the Multilevel Monte Carlo (MLMC) method. Our framework is built on reparameterized gradient estimators and "recycles" parameters obtained from past update history in optimization. In addition, our framework provides a new optimization algorithm …
We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG me…
Generalization in deep neural networks can be analyzed using minimax rates for gradient methods.
problem Generalization performance of over-parameterized neural networks
method Establishing a connection between gradient-based methods and kernel methods
result Deriving minimax-optimal rates for GD and SGD under polynomial network width scaling
Novel BSG method for efficient stochastic optimization.
problem Efficient optimization of non-convex surfaces in stochastic settings.
method Binary search combined with first order gradient optimization.
result BSG produces more promising results and better generalization than other methods.
Explains gradient descent methods and their convergence, focusing on simple analysis.
problem Understanding and analyzing gradient descent methods and their variants.
method Elementary mathematical analysis focusing on structures and assumptions of objective functions.
result Unified convergence analysis of various gradient descent methods and variants.
Policy gradient methods achieve linear convergence in simple MDPs.
problem Analyzing convergence rates of policy gradient methods in finite MDPs.
method Connections with policy iteration to show linear convergence with large step-sizes.
result Policy gradient methods succeed with large step-sizes and achieve linear rate of convergence.
Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving stochastic gradient methods named predictive local smoothness (PLS). First, we …
This paper studies Bayesian ranking and selection (R&S) problems with correlated prior beliefs and continuous domains, i.e. Bayesian optimization (BO). Knowledge gradient methods [Frazier et al., 2008, 2009] have been widely studied for discrete R&S problems, which sample the one-step Bayes-optimal point. When used ove…
New method for constrained sampling using gradient flows.
problem Sampling from constrained domains.
method Introducing a boundary condition for gradient flow to confine particles within the domain.
result Provable continuous-time convergence in total variation for constrained sampling.
Many machine learning, statistical inference, and portfolio optimization problems require minimization of a composition of expected value functions (CEVF). Of particular interest is the finite-sum versions of such compositional optimization problems (FS-CEVF). Compositional stochastic variance reduced gradient (C-SVRG)…
The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear ra…
Optimizes reinsurance and investment strategies to minimize ruin probability.
problem Optimizing reinsurance and investment strategies to minimize ruin probability.
method Stochastic projected gradient method based on Malliavin calculus.
result Effectiveness of the proposed method demonstrated through numerical experiments.
Quantized Adam reduces communication cost in deep learning training.
problem Reducing communication cost in distributed deep learning training.
method Gradient and weight quantization with error feedback in Adam.
result Proposed methods converge to first-order stationary points.
Stochastic gradient methods can converge in expectation under heavy-tailed noise.
problem Convergence of stochastic gradient methods under heavy-tailed noise.
method Comprehensive study of stochastic optimization under heavy-tailed noise for , , , in convex and nonconvex optimization.
result Established in-expectation convergence results for various stochastic gradient methods.
A new method for optimizing functions without gradients, improving efficiency and convergence.
problem Optimizing functions without gradient information in machine learning.
method Hybrid Gradient Descent (HGE) using random and coordinate-wise gradient estimates.
result The proposed method achieves optimal convergence rates in convex cases and generalizes to non-convex cases.