Related papers: Linear Convergence of Adaptive Stochastic Gradient…
Several variants of stochastic gradient descent (SGD) have been proposed to improve the learning effectiveness and efficiency when training deep neural networks, among which some recent influential attempts would like to adaptively control…
This paper studies some asymptotic properties of adaptive algorithms widely used in optimization and machine learning, and among them Adagrad and Rmsprop, which are involved in most of the blackbox deep learning algorithms. Our setup is the…
Conjugate gradient (CG) methods are a class of important methods for solving linear equations and nonlinear optimization problems. In this paper, we propose a new stochastic CG algorithm with variance reduction and we prove its linear…
Stochastic variance-reduced algorithms such as Stochastic Average Gradient (SAG) and SAGA, and their deterministic counterparts like the Incremental Aggregated Gradient (IAG) method, have been extensively studied in large-scale machine…
Adaptive gradient methods have been widely adopted in training large-scale deep neural networks, especially large foundation models. Despite the huge success in practice, their theoretical advantages over classical gradient methods with…
We provide a simple convergence proof for AdaGrad optimizing non-convex objectives under only affine noise variance and bounded smoothness assumptions. The proof is essentially based on a novel auxiliary function $\xi$ that helps eliminate…
We consider the problem of minimizing a convex function over a closed convex set, with Projected Gradient Descent (PGD). We propose a fully parameter-free version of AdaGrad, which is adaptive to the distance between the initialization and…
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…
Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process. To manage this realistic and challenging setting, new mechanisms, such as gradient clipping and gradient…
Minimax optimization recently is widely applied in many machine learning tasks such as generative adversarial networks, robust learning and reinforcement learning. In the paper, we study a class of nonconvex-nonconcave minimax optimization…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…
We present the remote stochastic gradient (RSG) method, which computes the gradients at configurable remote observation points, in order to improve the convergence rate and suppress gradient noise at the same time for different curvatures.…
Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the…
Adaptive gradient methods such as Adam have gained extreme popularity due to their success in training complex neural networks and less sensitivity to hyperparameter tuning compared to SGD. However, it has been recently shown that Adam can…
The vanilla fractional order gradient descent may oscillatively converge to a region around the global minimum instead of converging to the exact minimum point, or even diverge, in the case where the objective function is strongly convex.…
In this paper, we study the proximal incremental aggregated gradient(PIAG) algorithm for minimizing the sum of L-smooth nonconvex component functions and a proper closed convex function. By exploiting the L-smooth property and with the help…
This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It…
The asymptotic behavior of stochastic gradient algorithms is studied. Relying on results from differential geometry (Lojasiewicz gradient inequality), the single limit-point convergence of the algorithm iterates is demonstrated and…
Policy gradient (PG) methods have played an essential role in the empirical successes of reinforcement learning. In order to handle large state-action spaces, PG methods are typically used with function approximation. In this setting, the…
This paper considers the robust phase retrieval, which can be cast as a nonsmooth and nonconvex composite optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the…