Reproduce “The Randomized Midpoint Method for Log-Concave Sampling” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Ruoqi Shen, Yin Tat Lee
The randomized midpoint method estimates the gradient integral in each underdamped Langevin step by sampling an intermediate time and approximating its position there. Under smoothness and strong convexity, it reaches 2-Wasserstein error at most εD in \tilde O(κ^{7/6}ε^{-1/3}+κε^{-2/3}) iterations, versus \tilde O(κ^{1.5}/ε) previously. The theoretical guarantee applies to strongly log-concave, not arbitrary log-concave, targets.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.