arXiv research

Develops accelerated methods for optimization using low-dimensional projected-gradient information.

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…

Study on Nesterov's method in stochastic settings, revealing divergence under certain conditions.

Optimizes deep learning pipelines with novel algorithms for smooth and non-smooth functions.

AGNES accelerates gradient descent with noisy gradients.

Nesterov's extrapolation improves convergence in nonsmooth optimization.

In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration compl…

GPA improves LLM training speed by 8.71% for Llama-160M models.

Predictive models can be used on high-dimensional brain images for diagnosis of a clinical condition. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to …

Improved non-smooth optimization methods achieve faster convergence rates.

This research accelerates sampling methods using Nesterov's Acceleration.

Accelerated gradient method's stability deteriorates exponentially with steps.

Paper proposes an efficient online Newton method with Nesterov's acceleration for streaming data.

Two new differentially private optimization algorithms derived from accelerated methods.

In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in [8,11] for minimizing the sum of a smooth convex function and a block-separable convex function. In particular, we extend Nesterov's technique developed in [8] for analyzing the RBCD method for minimizing a smooth convex functio…

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimizati…

Continuized Nesterov acceleration accelerates stochastic gradient descent and gossip algorithms.

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…

Paper improves rates for solving smooth minimax optimization problems.

New dynamical system framework explains Nesterov acceleration.

Adapts SGD to noise and problem specifics for faster convergence.

Nesterov SGD is widely used for training modern neural networks and other machine learning models. Yet, its advantages over SGD have not been theoretically clarified. Indeed, as we show in our paper, both theoretically and empirically, Nesterov SGD with any parameter selection does not in general provide acceleration o…

Improved training of large-scale neural networks with reduced variance noise.

New method accelerates gradient descent on curved spaces.

State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothn…

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…

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 …

Novel method improves training RNNs by accelerating gradient descent.

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.

ANADDH uses deep learning to improve volatility risk management.

This paper improves NAQ method for faster convergence on Tensorflow.

Improved optimization guarantees for deep learning models with Nesterov acceleration.

A new algorithm improves convergence rates for convex optimization problems.

Symplectic discretization accelerates optimization of smooth convex functions.

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov's excessive gap te…

Unified analysis of Federated Averaging and Nesterov FedAvg for linear speedup.

Generalizes smoothness conditions for optimization methods.

GRU models with Adam optimizer outperform other combinations in stock market forecasting.

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…

We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal rate both in the deterministic and stochastic case and operates without knowledge …

Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between $X$ and $W^T H$ to model the Poisson noise or the Gaussian noise.…

In this letter, we introduce a distributed Nesterov method, termed as $\mathcal{ABN}$, that does not require doubly-stochastic weight matrices. Instead, the implementation is based on a simultaneous application of both row- and column-stochastic weights that makes this method applicable to arbitrary (strongly-connected…

This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak 2006]. The proposed algorithm efficiently escapes saddle points and finds approximate local minima for general smooth, nonconvex functions in only $\mathcal{\tilde{O}}(ε^{-3.5})$ stochastic gradien…

The paper refines optimization algorithms using Lyapunov functions and differential equations.

A new transformer model accelerates training with optimization techniques.

A Support Vector Method for multivariate performance measures was recently introduced by Joachims (2005). The underlying optimization problem is currently solved using cutting plane methods such as SVM-Perf and BMRM. One can show that these algorithms converge to an eta accurate solution in O(1/Lambda*e) iterations, wh…

Unified view of gradient-based algorithms for stochastic convex composite optimization.