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With the fast development of deep learning, it has become common to learn big neural networks using massive training data. Asynchronous Stochastic Gradient Descent (ASGD) is widely adopted to fulfill this task for its efficiency, which is,…
We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly…
A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational…
Novel convergence analyses are presented of Riemannian stochastic gradient descent (RSGD) on a Hadamard manifold. RSGD is the most basic Riemannian stochastic optimization algorithm and is used in many applications in the field of machine…
We propose a new per-layer adaptive step-size procedure for stochastic first-order optimization methods for minimizing empirical loss functions in deep learning, eliminating the need for the user to tune the learning rate (LR). The proposed…
Establishing a fast rate of convergence for optimization methods is crucial to their applicability in practice. With the increasing popularity of deep learning over the past decade, stochastic gradient descent and its adaptive variants…
We investigate the stochastic gradient descent (SGD) method where the step size lies within a banded region instead of being given by a fixed formula. The optimal convergence rate under mild conditions and large initial step size is proved.…
Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost. Recent algorithms, notably the stochastic variational inference performs local…
Sparsity regularized loss minimization problems play an important role in various fields including machine learning, data mining, and modern statistics. Proximal gradient descent method and coordinate descent method are the most popular…
Stochastic gradient descent~(SGD) and its variants have been the dominating optimization methods in machine learning. Compared to SGD with small-batch training, SGD with large-batch training can better utilize the computational power of…
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…
We showcase important features of the dynamics of the Stochastic Gradient Descent (SGD) in the training of neural networks. We present empirical observations that commonly used large step sizes (i) lead the iterates to jump from one side of…
A prevalent belief among optimization specialists is that linear convergence of gradient descent is contingent on the function growing quadratically away from its minimizers. In this work, we argue that this belief is inaccurate. We show…
In this paper, we investigate the impact of stochasticity and large stepsizes on the implicit regularisation of gradient descent (GD) and stochastic gradient descent (SGD) over diagonal linear networks. We prove the convergence of GD and…
The fluctuation effect of gradient expectation and variance caused by parameter update between consecutive iterations is neglected or confusing by current mainstream gradient optimization algorithms.Using this fluctuation effect, combined…
Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD)…
Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications. In this article we perform a rigorous strong error analysis for SGD optimization algorithms. In particular, we prove…
In this paper, we propose a simple variant of the original stochastic variance reduction gradient (SVRG), where hereafter we refer to as the variance reduced stochastic gradient descent (VR-SGD). Different from the choices of the snapshot…
This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…