Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlo

Krishna Balasubramanian, Sinho Chewi, Murat A Erdogdu, Adil Salim, Shunshi Zhang

Abstract: For the task of sampling from a density $\pi \propto \exp(-V)$ on $\R^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample w...