# Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Learning

## TL;DR

This paper provides a non-asymptotic convergence analysis of Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) for non-convex optimization, demonstrating its effectiveness with subsampling techniques in finding global minima.

## Contribution

It offers the first non-asymptotic convergence analysis of SGHMC in non-convex settings, improving upon prior theoretical results.

## Key findings

- Enhanced convergence guarantees for SGHMC in non-convex optimization
- Improved theoretical bounds over previous analyses
- Validation of SGHMC's effectiveness with subsampling techniques

## Abstract

Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) is a momentum version of stochastic gradient descent with properly injected Gaussian noise to find a global minimum. In this paper, non-asymptotic convergence analysis of SGHMC is given in the context of non-convex optimization, where subsampling techniques are used over an i.i.d dataset for gradient updates. Our results complement those of [RRT17] and improve on those of [GGZ18].