Stochastic Gradient Hamiltonian Monte Carlo for non-convex learning

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. In contrast to Raginsky et al. (2017) and Gao et al. (2021), our results are sharper in terms of step size, variance, and independent from the number of iterations.