In this paper, we present some new (in-)tractability results related to the integration problem in subspaces of the Wiener algebra over the $d$-dimensional unit cube. We show that intractability holds for multivariate integration in the standard Wiener algebra in the deterministic setting, in contrast to polynomial tractability in an unweighted subspace of the Wiener algebra recently shown by Goda (2023). Moreover, we prove that multivariate integration in the subspace of the Wiener algebra introduced by Goda is strongly polynomially tractable if we switch to the randomized setting, where we obtain a better $\varepsilon$-exponent than the one implied by the standard Monte Carlo method. We also identify subspaces in which multivariate integration in the deterministic setting are (strongly) polynomially tractable and we compare these results with the bound which can be obtained via Hoeffding's inequality.

翻译：本文针对$d$维单位立方体上维纳代数子空间中的积分问题，提出若干新的（不可）可计算性结果。我们证明在确定性设定下，标准维纳代数中的多元积分具有不可计算性，这与Goda（2023）最近在无权重维纳代数子空间中证明的多项式可计算性形成对比。此外，我们证明若转向随机化设定，Goda引入的维纳代数子空间中的多元积分具有强多项式可计算性，且获得的$\varepsilon$指数优于标准蒙特卡洛方法所隐含的指数。我们还确定了在确定性设定下具有（强）多项式可计算性的多元积分子空间，并将这些结果与通过霍夫丁不等式可获得的界进行了比较。