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We study the iteration complexity of stochastic gradient descent (SGD) for minimizing the gradient norm of smooth, possibly nonconvex functions. We provide several results, implying that the $\mathcal{O}(\epsilon^{-4})$ upper bound of…

Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization…

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

While standard reinforcement learning optimizes a single reward signal, many applications require optimizing a nonlinear utility $f(J_1^\pi,\dots,J_M^\pi)$ over multiple objectives, where each $J_m^\pi$ denotes the expected discounted…

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…

We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…

The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…

The aim of this paper is to deepen the convergence analysis of the scaled gradient projection (SGP) method, proposed by Bonettini et al. in a recent paper for constrained smooth optimization. The main feature of SGP is the presence of a…

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. This point of view covers the stochastic gradient…

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…

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…

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 consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…

We study Concave Constrained Markov Decision Processes (Concave CMDPs) where both the objective and constraints are defined as concave functions of the state-action occupancy measure. We propose the Variance-Reduced Primal-Dual Policy…

Policy gradient (PG) methods are a class of effective reinforcement learning algorithms, particularly when dealing with continuous control problems. They rely on fresh on-policy data, making them sample-inefficient and requiring…

The generalized conditional gradient method is a popular algorithm for solving composite problems whose objective function is the sum of a smooth function and a nonsmooth convex function. Many convergence analyses of the algorithm rely on…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

The non-asymptotic analysis of Stochastic Gradient Descent (SGD) typically yields bounds that decompose into a bias term and a variance term. In this work, we focus on the bias component and study the extent to which SGD can match the…

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…