Search Results for author: Matthew Zhang

Found 4 papers, 0 papers with code

Improved Discretization Analysis for Underdamped Langevin Monte Carlo

no code implementations16 Feb 2023 Matthew Zhang, Sinho Chewi, Mufan Bill Li, Krishnakumar Balasubramanian, Murat A. Erdogdu

As a byproduct, we also obtain the first KL divergence guarantees for ULMC without Hessian smoothness under strong log-concavity, which is based on a new result on the log-Sobolev constant along the underdamped Langevin diffusion.

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

no code implementations10 Feb 2022 Krishnakumar Balasubramanian, Sinho Chewi, Murat A. Erdogdu, Adil Salim, Matthew Zhang

For the task of sampling from a density $\pi \propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher information after $O( L^2 d^2/\varepsilon^2)$ iterations.

Analysis of Langevin Monte Carlo from Poincaré to Log-Sobolev

no code implementations23 Dec 2021 Sinho Chewi, Murat A. Erdogdu, Mufan Bill Li, Ruoqi Shen, Matthew Zhang

Classically, the continuous-time Langevin diffusion converges exponentially fast to its stationary distribution $\pi$ under the sole assumption that $\pi$ satisfies a Poincar\'e inequality.

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