<ul><li>This paper introduces a shifted composition rule to adapt coupling arguments to the Kullback-Leibler (KL) divergence.</li><li>The framework combines local error analysis and Girsanov's theorem to yield tight bounds and KL divergence guarantees.</li><li>It is applicable in cases of strongly log-concave, weakly log-concave, or log-Sobolev target distributions.</li><li>The results include KL guarantees for the randomized midpoint discretization of the Langevin diffusion.</li></ul>

Shifted Composition III: Local Error Framework for KL Divergence

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