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arXiv · 2105.14163

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

Sinho Chewi·Patrik Gerber·Chen Lu·Thibaut Le Gouic·Philippe Rigollet
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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.

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Sinho Chewi, Patrik Gerber, Chen Lu, Thibaut Le Gouic, Philippe Rigollet. 2021-05-29. The query complexity of sampling from strongly log-concave distributions in one dimension. https://arxiv.org/abs/2105.14163

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