相关论文: Convergence of Sign-based Random Reshuffling Algor…

In recent years, non-convex optimization problems are more often described by generalized $(L_0, L_1)$-smoothness assumption rather than standard one. Meanwhile, severely corrupted data used in these problems has increased the demand for…

An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…

The Stochastic Extragradient (SEG) method is one of the most popular algorithms for solving finite-sum min-max optimization and variational inequality problems (VIPs) appearing in various machine learning tasks. However, existing…

In machine learning and neural network optimization, algorithms like incremental gradient, and shuffle SGD are popular due to minimizing the number of cache misses and good practical convergence behavior. However, their optimization…

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.,…

We prove local convergence of several notable gradient descent algorithms used in machine learning, for which standard stochastic gradient descent theory does not apply directly. This includes, first, online algorithms for recurrent models…

Many machine learning tasks can be formulated as Regularized Empirical Risk Minimization (R-ERM), and solved by optimization algorithms such as gradient descent (GD), stochastic gradient descent (SGD), and stochastic variance reduction…

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…

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…

Stochastic gradient descent (SGD) algorithm is the method of choice in many machine learning tasks thanks to its scalability and efficiency in dealing with large-scale problems. In this paper, we focus on the shuffling version of SGD which…

We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on non-convex optimization. Recent studies have shown that the asynchronous stochastic…

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…

We study the performance of stochastic gradient descent (SGD) on smooth and strongly-convex finite-sum optimization problems. In contrast to the majority of existing theoretical works, which assume that individual functions are sampled with…

Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However,…

We combine two advanced ideas widely used in optimization for machine learning: shuffling strategy and momentum technique to develop a novel shuffling gradient-based method with momentum, coined Shuffling Momentum Gradient (SMG), for…

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

Traditional analyses in non-convex optimization typically rely on the smoothness assumption, namely requiring the gradients to be Lipschitz. However, recent evidence shows that this smoothness condition does not capture the properties of…

Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…

In this paper, we proposed a new technique, {\em variance controlled stochastic gradient} (VCSG), to improve the performance of the stochastic variance reduced gradient (SVRG) algorithm. To avoid over-reducing the variance of gradient by…

We study without-replacement SGD for solving finite-sum optimization problems. Specifically, depending on how the indices of the finite-sum are shuffled, we consider the RandomShuffle (shuffle at the beginning of each epoch) and…