Related papers: Kalman-based Stochastic Gradient Method with Stop …
We consider stochastic optimization of a smooth non-convex loss function with a convex non-smooth regularizer. In the online setting, where a single sample of the stochastic gradient of the loss is available at every iteration, the problem…
Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
Duality of control and estimation allows mapping recent advances in data-guided control to the estimation setup. This paper formalizes and utilizes such a mapping to consider learning the optimal (steady-state) Kalman gain when process and…
Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…
Recent empirical evidence indicates that many machine learning applications involve heavy-tailed gradient noise, which challenges the standard assumptions of bounded variance in stochastic optimization. Gradient clipping has emerged as a…
Stochastic Gradient Descent (SGD) is widely used in machine learning problems to efficiently perform empirical risk minimization, yet, in practice, SGD is known to stall before reaching the actual minimizer of the empirical risk. SGD…
In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimisation methods in machine learning, imaging and…
We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on…
In this paper, we study the convergence properties of the Stochastic Gradient Descent (SGD) method for finding a stationary point of a given objective function $J(\cdot)$. The objective function is not required to be convex. Rather, our…
We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations framework introduced by Li et al., we derive effective…
Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for…
This paper proposes a thorough theoretical analysis of Stochastic Gradient Descent (SGD) with non-increasing step sizes. First, we show that the recursion defining SGD can be provably approximated by solutions of a time inhomogeneous…
We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
We consider stochastic optimization problems where the objective depends on some parameter, as commonly found in hyperparameter optimization for instance. We investigate the behavior of the derivatives of the iterates of Stochastic Gradient…
Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…
The matrix completion problem seeks to recover a $d\times d$ ground truth matrix of low rank $r\ll d$ from observations of its individual elements. Real-world matrix completion is often a huge-scale optimization problem, with $d$ so large…
First-order methods like stochastic gradient descent(SGD) are recently the popular optimization method to train deep neural networks (DNNs), but second-order methods are scarcely used because of the overpriced computing cost in getting the…
We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the…