Related papers: Extended convexity and smoothness and their applic…
Decentralized optimization has become a fundamental tool for large-scale learning systems; however, most existing methods rely on the classical Lipschitz smoothness assumption, which is often violated in problems with rapidly varying…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
We identify and analyze a fundamental limitation of the classical projected subgradient method in nonsmooth convex optimization: the inevitable failure caused by the absence of valid subgradients at boundary points. We show that, under…
Stochastic Gradient Descent (SGD), a widely used optimization algorithm in deep learning, is often limited to converging to local optima due to the non-convex nature of the problem. Leveraging these local optima to improve model performance…
We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and…
Stochastic Gradient Descent (SGD) is a widely deployed optimization procedure throughout data-driven and simulation-driven disciplines, which has drawn a substantial interest in understanding its global behavior across a broad class of…
We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…
In federated distributed learning, the goal is to optimize a global training objective defined over distributed devices, where the data shard at each device is sampled from a possibly different distribution (a.k.a., heterogeneous or non…
In this paper, we show that simple {Stochastic} subGradient Decent methods with multiple Restarting, named {\bf RSGD}, can achieve a \textit{linear convergence rate} for a class of non-smooth and non-strongly convex optimization problems…
In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex…
Stochastic gradient methods for minimizing nonconvex composite objective functions typically rely on the Lipschitz smoothness of the differentiable part, but this assumption fails in many important problem classes like quadratic inverse…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
In centralized settings, it is well known that stochastic gradient descent (SGD) avoids saddle points and converges to local minima in nonconvex problems. However, similar guarantees are lacking for distributed first-order algorithms. The…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
In this paper, we investigate the theoretical properties of stochastic gradient descent (SGD) for statistical inference in the context of nonconvex optimization problems, which have been relatively unexplored compared to convex settings.…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a…
Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which…
Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…