相关论文: Gradient-Based Empirical Risk Minimization using L…

We consider the random design regression model with square loss. We propose a method that aggregates empirical minimizers (ERM) over appropriately chosen random subsets and reduces to ERM in the extreme case, and we establish sharp oracle…

Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…

We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient descent (GD) and stochastic gradient descent (SGD) with…

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

We study the problem of learning a low-degree spherical polynomial of degree $k_0 = \Theta(1) \ge 1$ defined on the unit sphere in $\RR^d$ by training an over-parameterized two-layer neural network with augmented feature in this paper. Our…

In this work, we consider the problem of a network of agents collectively minimizing a sum of convex functions. The agents in our setting can only access their local objective functions and exchange information with their immediate…

We give nearly matching upper and lower bounds on the oracle complexity of finding $\epsilon$-stationary points ($\| \nabla F(x) \| \leq\epsilon$) in stochastic convex optimization. We jointly analyze the oracle complexity in both the local…

In this paper, we study the generalization performance of global minima for implementing empirical risk minimization (ERM) on over-parameterized deep ReLU nets. Using a novel deepening scheme for deep ReLU nets, we rigorously prove that…

Pairwise learning, an important domain within machine learning, addresses loss functions defined on pairs of training examples, including those in metric learning and AUC maximization. Acknowledging the quadratic growth in computation…

A landmark result of non-smooth convex optimization is that gradient descent is an optimal algorithm whenever the number of computed gradients is smaller than the dimension $d$. In this paper we study the extension of this result to the…

Sharpness-aware Minimization (SAM) has been proposed recently to improve model generalization ability. However, SAM calculates the gradient twice in each optimization step, thereby doubling the computation costs compared to stochastic…

Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient…

This paper generalizes the optimized gradient method (OGM) that achieves the optimal worst-case cost function bound of first-order methods for smooth convex minimization. Specifically, this paper studies a generalized formulation of OGM and…

This work analyzes the convergence of a class of smoothing-based gradient descent methods when applied to optimization problems. In particular, Gaussian smoothing is employed to define a nonlocal gradient that reduces high-frequency noise,…

Incremental gradient and incremental proximal methods are a fundamental class of optimization algorithms used for solving finite sum problems, broadly studied in the literature. Yet, without strong convexity, their convergence guarantees…

This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…

The low-rank matrix recovery problem seeks to reconstruct an unknown $n_1 \times n_2$ rank-$r$ matrix from $m$ linear measurements, where $m\ll n_1n_2$. This problem has been extensively studied over the past few decades, leading to a…

We provide tight upper and lower bounds on the complexity of minimizing the average of $m$ convex functions using gradient and prox oracles of the component functions. We show a significant gap between the complexity of deterministic vs…

We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order…