# Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Learning

arXiv: https://arxiv.org/abs/1903.10328 · HTML: https://mlsanity.com/paper/1903.10328/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2019.

## Built on by (most cited first, 8 of 8)

- [Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case](https://mlsanity.com/paper/2301.08039/) (2023)
- [Kinetic Interacting Particle Langevin Monte Carlo](https://mlsanity.com/paper/2407.05790/) (2024)
- [Decentralized Bayesian Learning with Metropolis-Adjusted Hamiltonian Monte Carlo](https://mlsanity.com/paper/2107.07211/) (2021)
- [Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theory](https://mlsanity.com/paper/2407.06935/) (2024)
- [Hamiltonian Monte Carlo with Asymmetrical Momentum Distributions](https://mlsanity.com/paper/2110.12907/) (2021)
- [Error estimates between SGD with momentum and underdamped Langevin diffusion](https://mlsanity.com/paper/2410.17297/) (2024)
- [Contractive kinetic Langevin samplers beyond global Lipschitz continuity](https://mlsanity.com/paper/2509.12031/) (2025)
- [When Descent Is Too Stable: Event-Triggered Hamiltonian Learning to Optimize](https://mlsanity.com/paper/2605.06868/) (2026)

## Abstract (arXiv)

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].