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.

翻译：我们设定了美元( log\ log\ kappa) 的第一个紧要下限( $\ omega (\ log\ log\ kappa) $ ), 用于从强烈对数计算和对数间分布的类别中进行抽样的查询复杂性, 条件编号为 $\ kappa $ 。 以 $\ kappa 来保证基于 MC 的算法的多元比例, 以 $\ kappa 表示, 我们引入了基于拒绝抽样的新型算法, 以缩小这个双倍指数差距 。