相关论文: Convergence diagnostics for stochastic gradient de…

In recent years, there has been an intense debate about how learning in biological neural networks (BNNs) differs from learning in artificial neural networks. It is often argued that the updating of connections in the brain relies only on…

Data-driven iterative learning control can achieve high performance for systems performing repeating tasks without the need for modeling. The aim of this paper is to develop a fast data-driven method for iterative learning control that is…

Asynchronous stochastic gradient descent (ASGD) is a standard way to exploit heterogeneous compute resources in distributed learning: instead of forcing fast workers to wait for slow ones, the server updates the model whenever a gradient…

Stochastic Gradient Descent (SGD) plays a central role in modern machine learning. While there is extensive work on providing error upper bound for SGD, not much is known about SGD error lower bound. In this paper, we study the convergence…

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…

Optimization techniques are at the core of many scientific and engineering disciplines. The steepest descent methods play a foundational role in this area. In this paper we studied a generalized steepest descent method on Riemannian…

We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions. In particular, the results are…

In many derivative-free optimization algorithms, a sufficient decrease condition decides whether to accept a trial step in each iteration. This condition typically requires that the potential objective function value decrease of the trial…

Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…

In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective…

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear…

We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $\tau$ rounds ago. First, we show that without stochastic…

Computing the gradient of a function provides fundamental information about its behavior. This information is essential for several applications and algorithms across various fields. One common application that require gradients are…

In this paper, we propose a novel warm restart technique using a new logarithmic step size for the stochastic gradient descent (SGD) approach. For smooth and non-convex functions, we establish an $O(\frac{1}{\sqrt{T}})$ convergence rate for…

Modern machine learning focuses on highly expressive models that are able to fit or interpolate the data completely, resulting in zero training loss. For such models, we show that the stochastic gradients of common loss functions satisfy a…

We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a…

In this paper, we describe a new way to get convergence rates for optimal methods in smooth (strongly) convex optimization tasks. Our approach is based on results for tasks where gradients have nonrandom small noises. Unlike previous…

In this paper, we propose a new framework to study distributed optimization problems with stochastic gradients by employing a multi-agent system with continuous-time dynamics. Here the goal of the agents is to cooperatively minimize the sum…

In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We…

There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…