Related papers: AdaGDA: Faster Adaptive Gradient Descent Ascent Me…
Neural network training is inherently sequential where the layers finish the forward propagation in succession, followed by the calculation and back-propagation of gradients (based on a loss function) starting from the last layer. The…
Following the introduction of Adam, several novel adaptive optimizers for deep learning have been proposed. These optimizers typically excel in some tasks but may not outperform Adam uniformly across all tasks. In this work, we introduce…
This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of…
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,…
Adaptive gradient methods like AdaGrad are widely used in optimizing neural networks. Yet, existing convergence guarantees for adaptive gradient methods require either convexity or smoothness, and, in the smooth setting, only guarantee…
Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process. Distributed and asynchronous variants of gradient descent have been…
Nonconvex constrained optimization problems can be used to model a number of machine learning problems, such as multi-class Neyman-Pearson classification and constrained Markov decision processes. However, such kinds of problems are…
In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model…
Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such…
Gradient descent is slow to converge for ill-conditioned problems and non-convex problems. An important technique for acceleration is step-size adaptation. The first part of this paper contains a detailed review of step-size adaptation…
Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on…
Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…
Stochastic gradient descent-ascent (SGDA) is one of the main workhorses for solving finite-sum minimax optimization problems. Most practical implementations of SGDA randomly reshuffle components and sequentially use them (i.e.,…
We aim to make stochastic gradient descent (SGD) adaptive to (i) the noise $\sigma^2$ in the stochastic gradients and (ii) problem-dependent constants. When minimizing smooth, strongly-convex functions with condition number $\kappa$, we…
Minimax problems of the form $\min_x \max_y \Psi(x,y)$ have attracted increased interest largely due to advances in machine learning, in particular generative adversarial networks. These are typically trained using variants of stochastic…
Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In practically relevant training problems, usually not the plain…
Memory-efficient optimization methods have recently gained increasing attention for scaling full-parameter training of large language models under the GPU-memory bottleneck. Existing approaches either lack clear convergence guarantees, or…
An increasing number of machine learning problems, such as robust or adversarial variants of existing algorithms, require minimizing a loss function that is itself defined as a maximum. Carrying a loop of stochastic gradient ascent (SGA)…
In the paper, we propose a class of efficient adaptive bilevel methods based on mirror descent for nonconvex bilevel optimization, where its upper-level problem is nonconvex possibly with nonsmooth regularization, and its lower-level…
Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence…