The query complexity of sampling from strongly log-concave distributions in one dimension

05/29/2021

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by   Sinho Chewi, et al.

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We establish the first tight lower bound of Ω(loglogκ) on the query complexity of sampling from the class of strongly log-concave and log-smooth distributions with condition number κ in one dimension. Whereas existing guarantees for MCMC-based algorithms scale polynomially in κ, we introduce a novel algorithm based on rejection sampling that closes this doubly exponential gap.