Related papers: Adaptive Preconditioned Gradient Descent with Ener…
Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…
Adaptive gradient methods are the method of choice for optimization in machine learning and used to train the largest deep models. In this paper we study the problem of learning a local preconditioner, that can change as the data is…
Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC).…
First-order methods with momentum such as Nesterov's fast gradient method are very useful for convex optimization problems, but can exhibit undesirable oscillations yielding slow convergence rates for some applications. An adaptive…
In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam)…
Conditional stochastic optimization covers a variety of applications ranging from invariant learning and causal inference to meta-learning. However, constructing unbiased gradient estimators for such problems is challenging due to the…
We present a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our approach involves constructing a surrogate for the objective…
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…
Gradient descent (GD) is a collection of continuous optimization methods that have achieved immeasurable success in practice. Owing to data science applications, GD with diminishing step sizes has become a prominent variant. While this…
This paper introduces a novel approach to enhance the performance of the stochastic gradient descent (SGD) algorithm by incorporating a modified decay step size based on $\frac{1}{\sqrt{t}}$. The proposed step size integrates a logarithmic…
Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…
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)…
Most popular optimizers for deep learning can be broadly categorized as adaptive methods (e.g. Adam) and accelerated schemes (e.g. stochastic gradient descent (SGD) with momentum). For many models such as convolutional neural networks…
We focus on the problem of efficient sampling and learning of probability densities by incorporating symmetries in probabilistic models. We first introduce Equivariant Stein Variational Gradient Descent algorithm -- an equivariant sampling…
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…
In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation--namely, the need to compute or approximate Hessian…
We address the challenge of estimating the learning rate for adaptive gradient methods used in training deep neural networks. While several learning-rate-free approaches have been proposed, they are typically tailored for steepest descent.…
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…
We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the…