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The query complexity of sampling from strongly log-concave distributions in one dimension (2105.14163v2)
Published 29 May 2021 in math.ST, cs.LG, and stat.TH
Abstract: We establish the first tight lower bound of $\Omega(\log\log\kappa)$ on the query complexity of sampling from the class of strongly log-concave and log-smooth distributions with condition number $\kappa$ in one dimension. Whereas existing guarantees for MCMC-based algorithms scale polynomially in $\kappa$, we introduce a novel algorithm based on rejection sampling that closes this doubly exponential gap.