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Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the…
The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any…
We develop generalization error bounds for stochastic gradient descent (SGD) with label noise in non-convex settings under uniform dissipativity and smoothness conditions. Under a suitable choice of semimetric, we establish a contraction in…
Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
We are interested in gradient-based Explicit Generative Modeling where samples can be derived from iterative gradient updates based on an estimate of the score function of the data distribution. Recent advances in Stochastic Gradient…
Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGLD) serving as a key tool for scalable posterior sampling and decentralized variants enabling…
We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two…
In this article we investigate hypocoercivity of Langevin-type dynamics in nonlinear smooth geometries. The main result stating exponential decay to an equilibrium state with explicitly computable rate of convergence is rooted in an…
The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, and has gained attention recently as a model for the gradient descent dynamics of interacting…
Modern machine learning focuses on highly expressive models that are able to fit or interpolate the data completely, resulting in zero training loss. For such models, we show that the stochastic gradients of common loss functions satisfy a…
This paper provides a finite-sample analysis of a passive stochastic gradient Langevin dynamics (PSGLD) algorithm. This algorithm is designed to achieve adaptive inverse reinforcement learning (IRL). Adaptive IRL aims to estimate the cost…
Hogwild! implements asynchronous Stochastic Gradient Descent (SGD) where multiple threads in parallel access a common repository containing training data, perform SGD iterations and update shared state that represents a jointly learned…
Over the last decades, Stochastic Gradient Descent (SGD) has been intensively studied by the Machine Learning community. Despite its versatility and excellent performance, the optimization of large models via SGD still is a time-consuming…
In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can…
We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of…
We study gradient descent (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective,…
This paper analyzes the numerical approximation of the Lindblad master equation on infinite-dimensional Hilbert spaces. We employ a classical Galerkin approach for spatial discretization and investigate the convergence of the discretized…
Stochastic Gradient Descent (SGD) is a widely deployed optimization procedure throughout data-driven and simulation-driven disciplines, which has drawn a substantial interest in understanding its global behavior across a broad class of…
Modern machine learning is trained by stochastic gradient descent (SGD), whose performance critically depends on how the learning rate (LR) is adjusted and decreased over time. Yet existing LR regimes may be intricate, or need to tune one…