In this paper, we study and analyze zeroth-order stochastic approximation
algorithms for solving bilvel problems, when neither the upper/lower objective
values, nor their unbiased gradient estimates are available. In particular,
exploiting Stein's identity, we first use Gaussian smoothing to estimate first-
and second-order partial derivatives of functions with two independent block of
variables. We then used these estimates in the framework of a stochastic
approximation algorithm for solving bilevel optimization problems and establish
its non-asymptotic convergence analysis. To the best of our knowledge, this is
the first time that sample complexity bounds are established for a fully
stochastic zeroth-order bilevel optimization algorithm.

本文研究使用零阶随机逼近算法解决双层问题，无论是上 / 下目标值还是它们的无偏梯度估计都不可用。通过利用斯坦恩恒等式，首先使用高斯平滑估计具有两个独立块变量的函数的一阶和二阶偏导数。然后，在随机逼近算法框架中使用这些估计来解决双层优化问题，并建立其非渐近收敛分析。据我们所知，这是第一次为完全随机零阶双层优化算法建立样本复杂度界限。