Related papers: Stochastic Gradient/Mirror Descent: Minimax Optima…
A major obstacle to achieving global convergence in distributed and federated learning is the misalignment of gradients across clients, or mini-batches due to heterogeneity and stochasticity of the distributed data. In this work, we show…
In this paper, we investigate the theoretical properties of stochastic gradient descent (SGD) for statistical inference in the context of nonconvex optimization problems, which have been relatively unexplored compared to convex settings.…
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…
Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…
Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
We study Stochastic Gradient Descent (SGD) with diminishing step sizes for convex objective functions. We introduce a definitional framework and theory that defines and characterizes a core property, called curvature, of convex objective…
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and…
Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or ``stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large…
Theoretically understanding stochastic gradient descent (SGD) in overparameterized models has led to the development of several optimization algorithms that are widely used in practice today. Recent work by~\citet{zou2021benign} provides…
Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…
Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In…
The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…
While significant theoretical progress has been achieved, unveiling the generalization mystery of overparameterized neural networks still remains largely elusive. In this paper, we study the generalization behavior of shallow neural…
We study the implicit regularization of gradient descent towards structured sparsity via a novel neural reparameterization, which we call a diagonally grouped linear neural network. We show the following intriguing property of our…
Stochastic Gradient Descent (SGD) is a popular optimization method which has been applied to many important machine learning tasks such as Support Vector Machines and Deep Neural Networks. In order to parallelize SGD, minibatch training is…
Explaining the generalization characteristics of deep learning is an emerging topic in advanced machine learning. There are several unanswered questions about how learning under stochastic optimization really works and why certain…
Stochastic gradient optimization methods are broadly used to minimize non-convex smooth objective functions, for instance when training deep neural networks. However, theoretical guarantees on the asymptotic behaviour of these methods…
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…
Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of…