Ito Diffusion Approximation of Universal Ito Chains for Sampling, Optimization and Boosting

This work proposes a unified framework for analyzing a broad class of Markov chains, called Ito chains, which can model various sampling, optimization, and boosting algorithms. The authors provide bounds on the discretization error between the Ito chain and the corresponding Ito diffusion in the W2 distance, under weak and general assumptions on the chain's terms, including non-Gaussian and state-dependent noise.