Related papers: Stochastic Polyak Step-sizes and Momentum: Converg…
Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite…
We explore an explicit link between stochastic gradient descent using common batching strategies and splitting methods for ordinary differential equations. From this perspective, we introduce a new minibatching strategy (called Symmetric…
SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an…
In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…
This paper investigates the convergence properties of the hypergradient descent method (HDM), a 25-year-old heuristic originally proposed for adaptive stepsize selection in stochastic first-order methods. We provide the first rigorous…
Heavy ball momentum is crucial in accelerating (stochastic) gradient-based optimization algorithms for machine learning. Existing heavy ball momentum is usually weighted by a uniform hyperparameter, which relies on excessive tuning.…
In this paper, we propose a novel sufficient decrease technique for stochastic variance reduced gradient descent methods such as SVRG and SAGA. In order to make sufficient decrease for stochastic optimization, we design a new sufficient…
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
In this work, we investigate a stochastic gradient descent method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at…
Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…
We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to…
Two major momentum-based techniques that have achieved tremendous success in optimization are Polyak's heavy ball method and Nesterov's accelerated gradient. A crucial step in all momentum-based methods is the choice of the momentum…
The popular $\mathcal{AB}$/push-pull method for distributed optimization problem may unify much of the existing decentralized first-order methods based on gradient tracking technique. More recently, the stochastic gradient variant of…
Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for…
We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…
This is a short note on the performance of the ALI-G algorithm (Berrada et al., 2020) as reported in (Loizou et al., 2021). ALI-G (Berrada et al., 2020) and SPS (Loizou et al., 2021) are both adaptations of the Polyak step-size to optimize…
Block coordinate descent is a powerful algorithmic template suitable for big data optimization. This template admits a lot of variants including block gradient descent (BGD), which performs gradient descent on a selected block of variables,…
We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting…