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Sharp dimensional analysis of midpoint methods for Langevin sampling
We study deterministic and randomized midpoint discretizations of Langevin dynamics for a target $π\propto e^{-V}$, where $0 \prec αI\preceq\nabla^2V\preceqβI$ and $κ=β/α$. To achieve $\sqrtα\,W_2\leqslant\varepsilon$, we show that deterministic Heun uses at most $\widetilde O(κ^{4/3}d^{1/3}\varepsilon^{-2/3})$ gradien …