The efficient supervised training of artificial neural networks is commonly viewed as the minimization of an error function that depends on the weights of the network. This perspective gives some advantage to the development of effective training algorithms, because the problem of minimizing a function is well known in the field of numerical analysis. Typically, deterministic minimization metho...

We present various methods for inducing a conflict graph in order to effectively parallelize Pegasos. Pegasos is a stochastic sub-gradient descent algorithm for solving the Support Vector Machine (SVM) optimization problem [3]. In particular, we introduce a binary treebased conflict graph that matches convergence of a wellknown parallel implementation of stochastic gradient descent, know as HOG...

The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex neural networks use L1-regularization with the non-negative constraint. However, due to the difficulty of handling L1-regularization, these problems require ea...

Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset) at the end of each epoch. This limits the use of VR methods in practical dis...

Although many variants of stochastic gradient descent have been proposed for large-scale convex optimization, most of them require projecting the solution at each iteration to ensure that the obtained solution stays within the feasible domain. For complex domains (e.g., positive semidefinite cone), the projection step can be computationally expensive, making stochastic gradient descent unattrac...

We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in R. A simple and computationally cheap algorithm for this is stochastic gradient descent (SGD), which incrementally updates its estimate based on each new data point. However, due to the ...

In this paper we propose a simple and efficient method for improving stochastic gradient descent methods by using feedback from the objective function. The method tracks the relative changes in the objective function with a running average, and uses it to adaptively tune the learning rate in stochastic gradient descent. We specifically apply this idea to modify Adam, a popular algorithm for tra...

In many applications involving large dataset or online updating, stochastic gradient descent (SGD) provides a scalable way to compute parameter estimates and has gained increasing popularity due to its numerical convenience and memory efficiency. While the asymptotic properties of SGD-based estimators have been established decades ago, statistical inference such as interval estimation remains m...

Restart techniques are common in gradient-free optimization to deal with multimodal functions. Partial restarts are also gaining popularity in gradient-based optimization to improve the rate of convergence in accelerated gradient schemes to deal with ill-conditioned functions. In this paper, we propose a simple restart technique for stochastic gradient descent to improve its anytime performance...

1 Context Given a finite set of m examples z 1 ,. .. , z m and a strictly convex differen-tiable loss function ℓ(z, θ) defined on a parameter vector θ ∈ R d , we are interested in minimizing the cost function min θ C(θ) = 1 m m i=1 ℓ(z i , θ). One way to perform such a minimization is to use a stochastic gradient algorithm. Starting from some initial value θ[1], iteration t consists in picking ...