In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an entropy-like update-generating function, these algorithms perform gradient descent in the space equipped with the maximum norm, which allows us to exploit the low-dimensional structure of the decision sets for high-dimensional problems. Together with a sampling method based on the Rademacher distribution and variance reduction techniques, the proposed algorithms guarantee a logarithmic complexity dependence on dimensionality for zeroth-order optimisation problems.

翻译：在本文中,我们提出并分析一套通用的随机合成镜像回溯式算法。在适应性步数大小的情况下,提议的算法不需要事先了解问题。这些算法结合了一种类似酶式的更新生成功能,在配备了最大规范的空间里,具有梯度下降作用,从而使我们能够利用决策组的低维结构解决高维问题。除了基于Rademacher分布和差异减少技术的抽样方法外,提议的算法保证了对维度的逻辑复杂性依赖零顺序优化问题。