论文标题
非convex复合目标的自适应随机优化
Adaptive Stochastic Optimisation of Nonconvex Composite Objectives
论文作者
论文摘要
在本文中，我们提出和分析了一系列广义随机复合镜下降算法。凭借自适应步骤尺寸，提出的算法会收敛，而无需先验问题。这些算法结合了类似熵的更新生成功能，在配备了最大规范的空间中执行梯度下降，这使我们能够利用决策集的低维结构来解决高维问题。与基于Rademacher分布和降低方差降低技术的采样方法一起，提出的算法确保了对数的复杂性依赖于尺寸的对数，用于零好的订单优化问题。
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.
