面向鲁棒优化的集成梯度综述
Review of ensemble gradients for robust optimisation
AI总结：
本文重新审视 EnOpt 中的 StoSAG 集成梯度，严格解释配对导致的互相关问题，提出广义变体与去相关方法，并通过玩具问题和方差分析评估其鲁棒优化效果。
摘要：
在鲁棒优化问题中，目标函数由对（一个）不确定参数集合的平均值构成。集成优化（EnOpt）通过对控制参数（集合）的蒙特卡洛模拟进行线性回归来估计梯度，从而实现最速下降。将 EnOpt 应用于鲁棒优化的代价很高，除非对两个集合上的评估进行合并，即“配对”。本文对 EnOpt 中使用的随机单纯形近似梯度（StoSAG）提出了一个新的、更严格的视角，解释了它如何仅捕获由控制向量而非不确定参数向量引起的变率，从而处理配对产生的有害互相关。文中从一个广义推导中得到了若干次要变体，以及一种使用去相关的新方法。这些在线性和非线性玩具梯度估计问题上进行了测试；在这些问题中，它们取得了高度相似的精度，但当考虑方差而不仅是偏差时，需要非常大的集合规模才能优于非鲁棒方法。其他原创贡献包括讨论 EnOpt 所适用的特定鲁棒控制目标、示例说明、方差缩减视角，以及关于协方差和梯度估计中中心化的讨论。
英文摘要：
In robust optimisation problems the objective function consists of an average over (an ensemble of) uncertain parameters. Ensemble optimisation (EnOpt) implements steepest descent by estimating the gradient using linear regression on Monte-Carlo simulations of (an ensemble of) control parameters. Applying EnOpt for robust optimisation is costly unless the evaluations over the two ensembles are combined, i.e. 'paired'. Here, we provide a new and more rigorous perspective on the stochastic simplex approximate gradient (StoSAG) used in EnOpt, explaining how it addresses detrimental cross-correlations arising from pairing by only capturing the variability due to the control vector, and not the vector of uncertain parameters. A few minor variants are derived from a generalised derivation, as well as a new approach using decorrelation. These variants are tested on linear and non-linear toy gradient estimation problems, where they achieve highly similar accuracy, but require a very large ensemble size to outperform the non-robust approach when accounting for variance and not just bias. Other original contributions include a discussion of the particular robust control objectives for which EnOpt is suited, illustrations, a variance reduction perspective, and a discussion on the centring in covariance and gradient estimation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
