Related papers: Adaptive Learning Rates for Faster Stochastic Grad…
In this paper, we focus on the problem of minimizing a continuously differentiable convex objective function, $\min_x f(x)$. Recently, Malitsky (2020); Alacaoglu et al.(2023) developed an adaptive first-order method, GRAAL. This algorithm…
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are based on semi-definite programming (\textit{SDP}), which is generally…
Tuning step sizes is crucial for the stability and efficiency of optimization algorithms. While adaptive coordinate-wise step sizes have been shown to outperform scalar step size in first-order methods, their use in second-order methods is…
Stochastic gradient descent (SGD) is an inherently sequential training algorithm--computing the gradient at batch $i$ depends on the model parameters learned from batch $i-1$. Prior approaches that break this dependence do not honor them…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
For large scale learning problems, it is desirable if we can obtain the optimal model parameters by going through the data in only one pass. Polyak and Juditsky (1992) showed that asymptotically the test performance of the simple average of…
This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…
The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate…
This paper studies the last iterate of subgradient method with Polyak step size when applied to the minimization of a nonsmooth convex function with bounded subgradients. We show that the subgradient method with Polyak step size achieves a…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
The training of deep neural networks is inherently a nonconvex optimization problem, yet standard approaches such as stochastic gradient descent (SGD) require simultaneous updates to all parameters, often leading to unstable convergence and…
Due to its simplicity and outstanding ability to generalize, stochastic gradient descent (SGD) is still the most widely used optimization method despite its slow convergence. Meanwhile, adaptive methods have attracted rising attention of…
We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying…
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…
Adaptive gradient methods for stochastic optimization adjust the learning rate for each parameter locally. However, there is also a global learning rate which must be tuned in order to get the best performance. In this paper, we present a…
This paper addresses stochastic optimization in a streaming setting with time-dependent and biased gradient estimates. We analyze several first-order methods, including Stochastic Gradient Descent (SGD), mini-batch SGD, and time-varying…
In this paper, a new gradient-based optimization approach by automatically adjusting the learning rate is proposed. This approach can be applied to design non-adaptive learning rate and adaptive learning rate. Firstly, I will introduce the…
Step sizes in neural network training are largely determined using predetermined rules such as fixed learning rates and learning rate schedules. These require user input or expensive global optimization strategies to determine their…
While adversarial training and its variants have shown to be the most effective algorithms to defend against adversarial attacks, their extremely slow training process makes it hard to scale to large datasets like ImageNet. The key idea of…