Study on Nesterov's method in stochastic settings, revealing divergence under certain conditions.
problem Understanding Nesterov's method in stochastic settings, especially finite-sum.
method Analysis of Nesterov's accelerated gradient method in stochastic and finite-sum settings.
result Nesterov's method may diverge in finite-sum settings without additional conditions.
Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.
problem Improving the convergence rate of stochastic gradient descent and gossip algorithms.
method Introducing a continuized variant of Nesterov acceleration, which mixes variables continuously and takes gradient steps at random times.
result The continuized Nesterov acceleration achieves convergence rates similar to Nesterov's original acceleration but with random parameters.
We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show that the continuous time ODE allows for a better understanding of Nesterov's schem…
Nesterov SGD doesn't accelerate over SGD in over-parameterized learning.
problem Theoretical and practical acceleration of SGD with momentum in over-parameterized learning.
method Introducing a compensation term to Nesterov SGD, resulting in MaSS algorithm.
result MaSS converges for same step sizes as SGD and achieves accelerated convergence rates over SGD.
New dynamical system framework explains Nesterov acceleration.
problem Understanding Nesterov's accelerated gradient method.
method Dynamical system derivation without vanishing step size.
result Acceleration arises from discretizing an ODE with semi-implicit Euler.
Develops accelerated methods for optimization using low-dimensional projected-gradient information.
problem Optimization with low-dimensional projected-gradient information and Nesterov acceleration.
method Randomized-subspace Nesterov accelerated gradient methods for smooth convex and strongly convex optimization.
result Established accelerated oracle-complexity guarantees and unified basis for comparing sketch families.
Improved training of large-scale neural networks with reduced variance noise.
problem Training large-scale neural networks with high variance noise.
method Stochastic variance reduced Nesterov's Accelerated Quasi-Newton method (SVR-NAQ).
result Improved performance compared to conventional methods on benchmark problems.
A distributed Nesterov method for arbitrary graphs achieves faster convergence.
problem Optimizing distributed systems over arbitrary graphs.
method Distributed Nesterov method ABN and its variation FROZEN. result Achieves acceleration compared to state-of-the-art methods.
New method accelerates gradient descent on curved spaces.
problem Optimizing functions on curved Riemannian manifolds.
method Developed a novel geometric inequality to control metric distortion, enabling a Riemannian accelerated gradient method.
result Proposed the first global accelerated gradient method for Riemannian manifolds.
We present a unifying framework for adapting the update direction in gradient-based iterative optimization methods. As natural special cases we re-derive classical momentum and Nesterov's accelerated gradient method, lending a new intuitive interpretation to the latter algorithm. We show that a new algorithm, which we …
AGNES accelerates gradient descent with noisy gradients.
problem Minimizing smooth convex and strongly convex functions with noisy gradients.
method Generalization of Nesterov's accelerated gradient descent algorithm for noisy conditions.
result AGNES achieves acceleration for noisy gradients with a constant of proportionality up to 1.
Novel method improves training RNNs by accelerating gradient descent.
problem Vanishing and exploding gradient problems in RNNs training.
method Adaptive stochastic Nesterov accelerated quasi-Newton method.
result Improved performance in training RNNs with low per-iteration cost.
Poor (even random) starting points for learning/training/optimization are common in machine learning. In many settings, the method of Robbins and Monro (online stochastic gradient descent) is known to be optimal for good starting points, but may not be optimal for poor starting points -- indeed, for poor starting point…
Proposes a new stochastic quasi-Newton method with Nesterov's acceleration.
problem Improving convergence in large-scale non-convex optimization problems.
method Stochastic quasi-Newton method with Nesterov's accelerated gradient.
result Improved performance compared to classical and popular methods.
ANADDH uses deep learning to improve volatility risk management.
problem Traditional Vega hedging strategies are inadequate for rapidly changing markets.
method Combines distributional reinforcement learning with adaptive Nesterov acceleration.
result Significant performance gains over existing hedging techniques.
This paper improves NAQ method for faster convergence on Tensorflow.
problem Non-convex optimization problems.
method Modified Nesterov's Accelerated Quasi-Newton (NAQ) method on Tensorflow.
result mNAQ converges better and faster than first and second order optimizers.
Improved optimization guarantees for deep learning models with Nesterov acceleration.
problem Optimization in non-convex deep learning landscapes.
method Analysis of Nesterov acceleration in benignly non-convex landscapes.
result Identical guarantees can be obtained in optimization problems with weak geometric assumptions, especially in overparametrized deep learning.
A new algorithm improves convergence rates for convex optimization problems.
problem Convex optimization problems with finite-sum structure.
method Nesterov Accelerated Shuffling Gradient (NASG) integrating Nesterov's acceleration with different shuffling schemes.
result Improved convergence rate of O(1/T) for unified shuffling schemes.
Nesterov's extrapolation improves convergence in nonsmooth optimization.
problem Improving convergence rate in nonsmooth convex optimization.
method Nesterov's extrapolation applied to projected subgradient methods.
result Nesterov's extrapolation optimizes individual convergence for nonsmooth problems.
This research accelerates sampling methods using Nesterov's Acceleration.
problem Improving sampling efficiency in MCMC methods.
method Developed a Hessian-Free High-Resolution ODE reformulation of NAG-SC, injected noise, and discretized the diffusion process.
result Quantified acceleration beyond underdamped Langevin in W2 distance for log-strongly-concave targets. Unified analysis of Federated Averaging and Nesterov FedAvg for linear speedup.
problem Understanding convergence of FL algorithms under non-i.i.d. data and partial participation.
method Systematic study of convergence guarantees for FedAvg and Nesterov FedAvg under different conditions.
result Unified analysis of linear speedup for FedAvg and Nesterov FedAvg in various settings.
GRU models with Adam optimizer outperform other combinations in stock market forecasting.
problem Comparing optimization techniques for time series forecasting in LSTM and GRU networks.
method Examined Adam and Nesterov Accelerated Gradient (NAG) on LSTM and GRU models for stock market forecasting.
result GRU models with Adam optimizer produced the lowest RMSE and outperformed other combinations.
First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent, which yields primal progress, and mirror descent, which yields dual progress. W…
Paper proposes an efficient online Newton method with Nesterov's acceleration for streaming data.
problem Efficient inference of online Newton methods with robustness to noise and ill-conditioning.
method Online Newton method with Hessian averaging and Nesterov's accelerated sketch-and-project solver.
result Global almost-sure convergence and asymptotic normality of the last iterate with non-asymptotic convergence guarantees.
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.
A new transformer model accelerates training with optimization techniques.
problem Training deep neural networks efficiently and effectively.
method Interprets transformer layers as optimization steps, applying Nesterov acceleration.
result The new model outperforms existing models on benchmark datasets.
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.
We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal gradient scheme and a new homotopy strategy for smoothness parameter. By an appropriat…
Unified view of gradient-based algorithms for stochastic convex composite optimization.
problem Optimization of stochastic convex composite functions.
method Extend the concept of estimate sequence to cover various gradient-based methods.
result Generic convergence proof and new adaptive SVRG variant.
Accelerates MMLE using SVGD with Nesterov acceleration.
problem Maximum Marginal Likelihood Estimation optimization.
method Stein variational gradient descent with Nesterov acceleration.
result Consistently accelerates convergence across various tasks.
New algorithm preserves symplectic structure for faster optimization.
problem Optimization methods in machine learning.
method Structure-preserving discretizations of dissipative Hamiltonian systems.
result Proposes a new algorithm that generalizes Nesterov and heavy ball methods.
Two new differentially private optimization algorithms derived from accelerated methods.
problem Improving privacy in optimization algorithms while maintaining convergence rates.
method Polyak's heavy ball method and Nesterov's accelerated gradient method with differential privacy.
result The proposed algorithms outperform existing differentially private optimization methods.
New methods improve adversarial attacks' transferability to other models.
problem Vulnerability of deep learning models to adversarial examples.
method Nesterov Iterative Fast Gradient Sign Method (NI-FGSM) and Scale-Invariant attack Method (SIM).
result NI-FGSM and SIM generate more transferable adversarial examples.
Proposes momentum methods for Lie groups, improving on classical algorithms.
problem Optimization on nonlinear spaces, especially Lie groups.
method Generalizes Nesterov's Accelerated Gradient method to Lie groups.
result Demonstrates faster convergence for NAG-like methods on Lie groups.
Improved SDE-BNN model reduces NFEs and accelerates convergence.
problem High computational cost and convergence instability in SDE-BNNs.
method Nesterov's Accelerated Gradient (NAG) method integrated into SDE-BNN framework.
result Significantly reduced number of function evaluations (NFEs) and improved predictive accuracy.
Nesterov's momentum trick is famously known for accelerating gradient descent, and has been proven useful in building fast iterative algorithms. However, in the stochastic setting, counterexamples exist and prevent Nesterov's momentum from providing similar acceleration, even if the underlying problem is convex and fin…
Stacking improves deep neural network training efficiency.
problem Improving the efficiency of training deep neural networks.
method Proposes stacking as a form of accelerated gradient descent.
result Proves stacking provides accelerated training for certain deep linear residual networks.
New algorithm AG-OG optimizes separable convex-concave problems efficiently.
problem Efficiently solving separable convex-concave minimax optimization problems.
method Leverages Nesterov acceleration and optimistic gradient on component and coupling parts of the problem.
result Achieves optimal convergence rate for various settings including bilinearly coupled problems.
We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a conv…
FedNAG improves federated learning accuracy and reduces training time.
problem Efficiency of federated learning with gradient descent.
method Nesterov Accelerated Gradient (NAG) applied to federated learning (FL) with additional momentum and model aggregation.
result FedNAG increases learning accuracy by 3-24% and reduces training time by 11-70%.
Accelerated optimization on curved geometry analyzed.
problem Understanding the accelerated gradient method in curved spaces.
method Geometric interpretation of AGM on Riemannian manifold, continuous time ODE analysis.
result Convergence rate analysis of ODE for quadratic objectives.
Two accelerated extragradient methods converge at O(1/k) rate for co-hypomonotone inclusions.
problem Solving co-hypomonotone inclusions with sum of Lipschitz and multivalued operators.
method Developed two Nesterov's accelerated extragradient methods for co-hypomonotone inclusions.
result Achieve O(1/k) last-iterate convergence rates on the residual norm. Optimizes deep learning pipelines with novel algorithms for smooth and non-smooth functions.
problem Optimizing deep learning pipelines for smooth and non-smooth functions.
method Provided matching lower and upper bounds for smooth convex and non-convex functions, and developed PPRS for non-smooth convex functions.
result PPRS achieves near-linear speed-up and convergence time for non-smooth non-convex problems.
Recently, {\it stochastic momentum} methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the gap between practice and theory by developing a basic convergence analysis of t…
New ODEs reveal key differences in accelerated gradient methods.
problem Understanding the acceleration phenomenon in optimization algorithms.
method Developed high-resolution ODEs to distinguish between NAG-SC and Polyak's heavy-ball method.
result Identified a gradient correction term in NAG-SC not present in Polyak's method.
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.
Develops mathematical framework for analyzing stochastic gradient algorithms.
problem Analyzing the dynamics of stochastic gradient algorithms.
method Stochastic modified equations (SME) framework to approximate stochastic gradient algorithms as stochastic differential equations.
result Proves that the approximation leads to precise results on SGD, momentum SGD, and Nesterov's accelerated gradient method.
A new gradient descent method speeds up in flat regions and slows in steep directions.
problem Improving the speed and stability of gradient descent algorithms.
method Introducing a 'power gradient' where each gradient component is replaced by its H-th power, with 0<H<1. result The new gradient descent methods achieve significantly better performances, especially for Nesterov accelerated gradient and AMSGrad.