Related papers: Natasha 2: Faster Non-Convex Optimization Than SGD
Adaptive optimizers can reduce to normalized steepest descent (NSD) when only adapting to the current gradient, suggesting a close connection between the two algorithmic families. A key distinction between their analyses, however, lies in…
Recently, local SGD has got much attention and been extensively studied in the distributed learning community to overcome the communication bottleneck problem. However, the superiority of local SGD to minibatch SGD only holds in quite…
We study the performance of stochastic gradient descent (SGD) on smooth and strongly-convex finite-sum optimization problems. In contrast to the majority of existing theoretical works, which assume that individual functions are sampled with…
The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have…
Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…
This paper studies decentralized optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};{\boldsymbol \xi}_i)\right]$ which is…
While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper…
In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm,…
In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use…
Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…
Nonconvex-concave min-max problem arises in many machine learning applications including minimizing a pointwise maximum of a set of nonconvex functions and robust adversarial training of neural networks. A popular approach to solve this…
We consider minimization of a smooth nonconvex objective function using an iterative algorithm based on Newton's method and the linear conjugate gradient algorithm, with explicit detection and use of negative curvature directions for the…
Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…
Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…
In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…
We study the problem of finding an $\epsilon$-first-order stationary point (FOSP) of a smooth function, given access only to gradient information. The best-known gradient query complexity for this task, assuming both the gradient and…
Memory-efficient optimization methods have recently gained increasing attention for scaling full-parameter training of large language models under the GPU-memory bottleneck. Existing approaches either lack clear convergence guarantees, or…
We study the first-order convex optimization problem, where we have black-box access to a (not necessarily smooth) function $f:\mathbb{R}^n \to \mathbb{R}$ and its (sub)gradient. Our goal is to find an $\epsilon$-approximate minimum of $f$…
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…