Related papers: Learning Orthogonal Multi-Index Models: A Fine-Gra…

Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…

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…

Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems. However, computing gradients via implicit differentiation requires solving a linear system with Hessian terms, which is…

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Arguably the biggest challenge in applying neural networks is tuning the hyperparameters, in particular the learning rate. The sensitivity to the learning rate is due to the reliance on backpropagation to train the network. In this paper we…

We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable,…

We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable dataset. The classifier is described by a nonlinear ReLU model and the objective function adopts the exponential…

In this paper, we propose a method of distributed stochastic gradient descent (SGD), with low communication load and computational complexity, and still fast convergence. To reduce the communication load, at each iteration of the algorithm,…

Graph neural network models have been extensively used to learn node representations for graph structured data in an end-to-end setting. These models often rely on localized first order approximations of spectral graph convolutions and…

This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…

We study the problem of online learning in contextual bandit problems where the loss function is assumed to belong to a known parametric function class. We propose a new analytic framework for this setting that bridges the Bayesian theory…

We investigate the fundamental optimization question of minimizing a target function $f$, whose gradients are expensive to compute or have limited availability, given access to some auxiliary side function $h$ whose gradients are cheap or…

We study the iteration complexity of stochastic gradient descent (SGD) for minimizing the gradient norm of smooth, possibly nonconvex functions. We provide several results, implying that the $\mathcal{O}(\epsilon^{-4})$ upper bound of…

This work focuses on the gradient flow dynamics of a neural network model that uses correlation loss to approximate a multi-index function on high-dimensional standard Gaussian data. Specifically, the multi-index function we consider is a…

Directed Exploration is a crucial challenge in reinforcement learning (RL), especially when rewards are sparse. Information-directed sampling (IDS), which optimizes the information ratio, seeks to do so by augmenting regret with information…

Stochastic gradient descent (SGD) is a workhorse algorithm for solving large-scale optimization problems in data science and machine learning. Understanding the convergence of SGD is hence of fundamental importance. In this work we examine…

The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…

We study the optimization and sample complexity of gradient-based training of a two-layer neural network with quadratic activation function in the high-dimensional regime, where the data is generated as $f_*(\boldsymbol{x}) \propto…

In this paper we analyze the necessary number of samples to estimate the gradient of any multidimensional smooth (possibly non-convex) function in a zero-order stochastic oracle model. In this model, an estimator has access to noisy values…

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more…