Related papers: Gradient-Based Empirical Risk Minimization using L…

Regularization is a widely recognized technique in mathematical optimization. It can be used to smooth out objective functions, refine the feasible solution set, or prevent overfitting in machine learning models. Due to its simplicity and…

Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…

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…

In this paper, the solution to the empirical risk minimization problem with $f$-divergence regularization (ERM-$f$DR) is presented and conditions under which the solution also serves as the solution to the minimization of the expected…

Reinforcement Learning (RL) has shown exceptional performance across various applications, enabling autonomous agents to learn optimal policies through interaction with their environments. However, traditional RL frameworks often face…

It is known that when the statistical models are singular, i.e., the Fisher information matrix at the true parameter is degenerate, the fixed step-size gradient descent algorithm takes polynomial number of steps in terms of the sample size…

The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function,…

This paper studies decentralized optimization over a compact submanifold within a communication network of $n$ nodes, where each node possesses a smooth non-convex local cost function, and the goal is to jointly minimize the sum of these…

Stochastic gradient descent plays a fundamental role in nearly all applications of deep learning. However its ability to converge to a global minimum remains shrouded in mystery. In this paper we propose to study the behavior of the loss…

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…

We present an extension of Vapnik's classical empirical risk minimizer (ERM) where the empirical risk is replaced by a median-of-means (MOM) estimator, the new estimators are called MOM minimizers. While ERM is sensitive to corruption of…

This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based algorithms may vary depending on the learning task, they behave…

We study the generalization properties of the popular stochastic optimization method known as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the…

We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…

In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of…

In this paper, we study the implicit regularization of the gradient descent algorithm in homogeneous neural networks, including fully-connected and convolutional neural networks with ReLU or LeakyReLU activations. In particular, we study…

The gradient descent (GD) method has been used widely to solve parameter estimation in generalized linear models (GLMs), a generalization of linear models when the link function can be non-linear. In GLMs with a polynomial link function, it…

The development of new classification and regression algorithms based on empirical risk minimization (ERM) over deep neural network hypothesis classes, coined deep learning, revolutionized the area of artificial intelligence, machine…

In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce…

Communication has been seen as a significant bottleneck in industrial applications over large-scale networks. To alleviate the communication burden, sign-based optimization algorithms have gained popularity recently in both industrial and…