Related papers: AI-SARAH: Adaptive and Implicit Stochastic Recursi…

In this work, we propose new adaptive step size strategies that improve several stochastic gradient methods. Our first method (StoPS) is based on the classical Polyak step size (Polyak, 1987) and is an extension of the recent development of…

In this paper, we propose a novel algorithm named STOchastic Recursive Momentum for Policy Gradient (STORM-PG), which operates a SARAH-type stochastic recursive variance-reduced policy gradient in an exponential moving average fashion.…

Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…

We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis of the constant-stepsize PG method, achieving the…

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function $F(w)=\frac{1}{n}…

We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…

In this paper we propose several adaptive gradient methods for stochastic optimization. Unlike AdaGrad-type of methods, our algorithms are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of…

We prove that the iterates produced by, either the scalar step size variant, or the coordinatewise variant of AdaGrad algorithm, are convergent sequences when applied to convex objective functions with Lipschitz gradient. The key insight is…

Adaptive gradient methods such as AdaGrad and its variants update the stepsize in stochastic gradient descent on the fly according to the gradients received along the way; such methods have gained widespread use in large-scale optimization…

Gradient descent is the primary workhorse for optimizing large-scale problems in machine learning. However, its performance is highly sensitive to the choice of the learning rate. A key limitation of gradient descent is its lack of natural…

We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…

Iteration complexities for optimizing smooth functions with first-order algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are then achieved using fixed step sizes. But many…

Q-learning and SARSA are foundational reinforcement learning algorithms whose practical success depends critically on step-size calibration. Step-sizes that are too large can cause numerical instability, while step-sizes that are too small…

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Motivated by neural network training in finite-precision arithmetic environments, this work studies the convergence of perturbed iterate SGD using adaptive step sizes in an environment with numerical error. Considering a general stochastic…

Establishing a fast rate of convergence for optimization methods is crucial to their applicability in practice. With the increasing popularity of deep learning over the past decade, stochastic gradient descent and its adaptive variants…

Shuffling-type gradient methods are favored in practice for their simplicity and rapid empirical performance. Despite extensive development of convergence guarantees under various assumptions in recent years, most require the Lipschitz…

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…

Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…

Stochastic optimization algorithms are widely used for machine learning with large-scale data. However, their convergence often suffers from non-vanishing variance. Variance Reduction (VR) methods, such as SVRG and SARAH, address this issue…