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New bounds established for Moreau--Yosida unadjusted Langevin sampling

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Researchers have established near-linear accuracy bounds for the Moreau--Yosida unadjusted Langevin algorithm (MYULA). The analysis provides an explicit step-size condition under which the invariant-measure bias relative to the Moreau-smoothed target is bounded by \(\\widetilde O(h)\\). This work combines the Moreau approximation bias with Wasserstein contraction to determine that \(\\widetilde O(\\varepsilon^{-1})\\) iterations are sufficient to achieve a desired accuracy for the Nth-iterate law. The stationary error is bounded directly, without requiring third derivatives or a Lipschitz Hessian, utilizing a Poisson-based estimate to convert a second-order stationary residual into a Wasserstein bound. AI

IMPACT Establishes theoretical bounds for sampling algorithms, potentially improving efficiency in machine learning model training.

RANK_REASON This is a research paper detailing theoretical advancements in sampling algorithms. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New bounds established for Moreau--Yosida unadjusted Langevin sampling

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This is a research paper detailing theoretical advancements in sampling algorithms. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Yuchen Xin, Zhihua Zhang ·

    Near-Linear Accuracy Bounds for Moreau--Yosida Unadjusted Langevin Sampling

    arXiv:2609.40193v1 Announce Type: new Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with Lipschitz gradient and …

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