相关论文: Infinity Learning: Learning Markov Chains from Agg…

Continuous-time models provide important insights into the training dynamics of optimization algorithms in deep learning. In this work, we establish a non-asymptotic convergence analysis of stochastic gradient Langevin dynamics (SGLD),…

It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and -- in asynchronous implementations -- on the gradient staleness. Especially, it has been…

We present a variational method for online state estimation and parameter learning in state-space models (SSMs), a ubiquitous class of latent variable models for sequential data. As per standard batch variational techniques, we use…

This study introduces a novel approach for learning mixtures of Markov chains, a critical process applicable to various fields, including healthcare and the analysis of web users. Existing research has identified a clear divide in…

We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive…

In this paper, we examine the long-run distribution of stochastic gradient descent (SGD) in general, non-convex problems. Specifically, we seek to understand which regions of the problem's state space are more likely to be visited by SGD,…

Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…

With the vigorous development of artificial intelligence technology, various engineering technology applications have been implemented one after another. The gradient descent method plays an important role in solving various optimization…

Asynchronous stochastic gradient descent (SGD) is attractive from a speed perspective because workers do not wait for synchronization. However, the Transformer model converges poorly with asynchronous SGD, resulting in substantially lower…

Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-horses for modern machine learning algorithms. Their constant stepsize variants are preferred in practice due to fast convergence behavior. However,…

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…

Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…

The convergence behavior of Stochastic Gradient Descent (SGD) crucially depends on the stepsize configuration. When using a constant stepsize, the SGD iterates form a Markov chain, enjoying fast convergence during the initial transient…

Traditional methods for solving linear systems have quickly become impractical due to an increase in the size of available data. Utilizing massive amounts of data is further complicated when the data is incomplete or has missing entries. In…

Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of work on SGD, much less is known…

When applied to training deep neural networks, stochastic gradient descent (SGD) often incurs steady progression phases, interrupted by catastrophic episodes in which loss and gradient norm explode. A possible mitigation of such events is…

Temporal-difference learning with gradient correction (TDC) is a two time-scale algorithm for policy evaluation in reinforcement learning. This algorithm was initially proposed with linear function approximation, and was later extended to…

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…

Modern deep neural networks (DNNs) are typically trained with a global cross-entropy loss in a supervised end-to-end manner: neurons need to store their outgoing weights; training alternates between a forward pass (computation) and a…

It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of…