Improved bounds for discretization of Langevin diffusions: Near-optimal rates without convexity
نویسندگان
چکیده
Discretizations of the Langevin diffusion have been proven very useful for developing and analyzing algorithms sampling stochastic optimization. We present an improved non-asymptotic analysis Euler-Maruyama discretization diffusion. Our does not require global contractivity, yields polynomial dependence on time horizon. Compared to existing approaches, we make additional smoothness assumption, improve rate in step size from O(η) O(η2) terms KL divergence. This result matches correct order numerical SDEs, without suffering exponential dependence. When applied MCMC, this simultaneously improves analyses a range that are based Dalalyan’s approach.
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2022
ISSN: ['1573-9759', '1350-7265']
DOI: https://doi.org/10.3150/21-bej1343