Related papers: Mini-Batch Primal and Dual Methods for SVMs
Stochastic gradient descent-ascent (SGDA) is one of the main workhorses for solving finite-sum minimax optimization problems. Most practical implementations of SGDA randomly reshuffle components and sequentially use them (i.e.,…
In this paper we develop dual free mini-batch SDCA with adaptive probabilities for regularized empirical risk minimization. This work is motivated by recent work of Shai Shalev-Shwartz on dual free SDCA method, however, we allow a…
We present a dual subspace ascent algorithm for support vector machine training that respects a budget constraint limiting the number of support vectors. Budget methods are effective for reducing the training time of kernel SVM while…
The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…
The stochastic proximal point (SPP) methods have gained recent attention for stochastic optimization, with strong convergence guarantees and superior robustness to the classic stochastic gradient descent (SGD) methods showcased at little to…
We analyze Local SGD (aka parallel or federated SGD) and Minibatch SGD in the heterogeneous distributed setting, where each machine has access to stochastic gradient estimates for a different, machine-specific, convex objective; the goal is…
In this work, we consider strongly convex strongly concave (SCSC) saddle point (SP) problems $\min_{x\in\mathbb{R}^{d_x}}\max_{y\in\mathbb{R}^{d_y}}f(x,y)$ where $f$ is $L$-smooth, $f(.,y)$ is $\mu$-strongly convex for every $y$, and…
Local SGD is a promising approach to overcome the communication overhead in distributed learning by reducing the synchronization frequency among worker nodes. Despite the recent theoretical advances of local SGD in empirical risk…
The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of $n$ local cost functions by using local information exchange is considered. This problem is an important component of many machine…
We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…
Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received…
Block coordinate descent (BCD) methods and their variants have been widely used in coping with large-scale nonconstrained optimization problems in many fields such as imaging processing, machine learning, compress sensing and so on. For…
Stochastic gradient descent~(SGD) and its variants have been the dominating optimization methods in machine learning. Compared to SGD with small-batch training, SGD with large-batch training can better utilize the computational power of…
A popular heuristic method for improving clustering results is to apply dimensionality reduction before running clustering algorithms. It has been observed that spectral-based dimensionality reduction tools, such as PCA or SVD, improve the…
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…
We extend the Approximate-Proximal Point (aProx) family of model-based methods for solving stochastic convex optimization problems, including stochastic subgradient, proximal point, and bundle methods, to the minibatch and accelerated…
The growing size of available data has attracted increasing interest in solving minimax problems in a decentralized manner for various machine learning tasks. Previous theoretical research has primarily focused on the convergence rate and…
We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…
We analyze the dynamics of large batch stochastic gradient descent with momentum (SGD+M) on the least squares problem when both the number of samples and dimensions are large. In this setting, we show that the dynamics of SGD+M converge to…
Stochastic Gradient Descent-Ascent (SGDA) is one of the most prominent algorithms for solving min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. The success of the method led to…