Related papers: Escaping Saddle Points with Compressed SGD
In this paper, we give a sharp analysis for Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point in…
This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…
We consider large scale distributed optimization over a set of edge devices connected to a central server, where the limited communication bandwidth between the server and edge devices imposes a significant bottleneck for the optimization…
Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…
We analyze stochastic gradient algorithms for optimizing nonconvex problems. In particular, our goal is to find local minima (second-order stationary points) instead of just finding first-order stationary points which may be some bad…
Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification,…
Huge scale machine learning problems are nowadays tackled by distributed optimization algorithms, i.e. algorithms that leverage the compute power of many devices for training. The communication overhead is a key bottleneck that hinders…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
We propose a novel algorithm for distributed stochastic gradient descent (SGD) with compressed gradient communication in the parameter-server framework. Our gradient compression technique, named flattened one-bit stochastic gradient descent…
We investigate the problem of finding second-order stationary points (SOSP) in differentially private (DP) stochastic non-convex optimization. Existing methods suffer from two key limitations: (i) inaccurate convergence error rate due to…
Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…
In centralized settings, it is well known that stochastic gradient descent (SGD) avoids saddle points and converges to local minima in nonconvex problems. However, similar guarantees are lacking for distributed first-order algorithms. The…
We develop two compression based stochastic gradient algorithms to solve a class of non-smooth strongly convex-strongly concave saddle-point problems in a decentralized setting (without a central server). Our first algorithm is a…
Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…
Stochastic gradient descent (SGD) is one of the most widely used optimization methods for solving various machine learning problems. SGD solves an optimization problem by iteratively sampling a few data points from the input data, computing…
We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…
Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…
In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…