基于置信度的自适应采样排序用于噪声黑箱优化
Confidence-based Ranking with Adaptive Sampling for Noisy Black-Box Optimisation
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中文总结 AI 辅助
针对噪声黑箱优化问题，提出基于置信度的自适应采样排序方法，采用计算高效的显式平均策略及采样预算自适应，在CMA - ES和GA框架中实现，经测试在同方差和异方差噪声问题上性能优于现有方法。
中文摘要 AI 辅助
现实世界中的优化问题常涉及黑箱函数及评估中的不确定性，即噪声优化问题（NOPs）。进化算法（EA）常被用于解决此类问题，但计算成本高。NOPs的适应度估计常用隐式平均和显式平均两种基本方法，隐式平均虽有理论优势但性能依赖特定假设，且多数现有算法只考虑同方差噪声。为解决这些问题，我们引入一组异方差测试问题，提出一种新颖的置信度排序方法，该方法采用计算高效的显式平均策略及采样预算自适应，在协方差矩阵自适应进化策略（CMA - ES）和遗传算法框架中实现，经测试在同方差和异方差噪声问题上均表现优异。
英文摘要
Real-world optimization problems often involve black-box functions and uncertainties in their evaluation, widely referred to as noisy optimization problems (NOPs). Evolutionary algorithms (EA), including Evolutionary Strategies (ES) and genetic algorithms (GA) have been commonly adopted to solve these problems in the contemporary literature. An ongoing challenge is the computational expense involved, given the number of evaluations required for good fitness estimation and ranking. Two fundamental methods commonly used for fitness estimation for NOPs are implicit averaging and explicit averaging. Explicit averaging uses resampling of solutions to improve the estimates, while implicit averaging typically uses a large population size with low resampling. Implicit averaging has been shown to have theoretical advantages for certain cases, which has motivated some recent approaches to use them. However, a recent study demonstrated that its performance is highly dependent on certain assumptions about the function, such as steepness and constant noise level, which may not apply for majority of the real world problems. Moreover, most existing algorithms have only considered homoscedastic noise, where the amplitude of variation is uniform across the entire search space, as opposed to more generic case of heteroscedastic noise. To address these issues, we introduce a set of heteroscedastic test problems and propose a novel confidence ranking method that employs a computationally efficient explicit averaging strategy with sampling budget adaptation. It is implemented within the Covariance Matrix Adaptation ES (CMA-ES) and GA frameworks to demonstrate its effectiveness and versatility. The resulting algorithm is evaluated on a range of problems with both homoscedastic and heteroscedastic noise, and it demonstrates superior performance compared to state-of-the-art approaches.
