用概率数值方法提升进化策略采样效率，让优化更快更准。
Natural Evolutionary Search meets Probabilistic Numerics
- 将贝叶斯积分融入自然进化策略，用概率方法替代随机采样
- 在各类任务中均优于传统进化算法和贝叶斯优化，样本效率更高
- 适合需要高效优化且有先验知识的场景，如超参调优与强化学习
零阶局部优化算法在求解实值黑箱优化问题中至关重要。其中，自然进化策略（NES）因其能融合先验分布，在半监督学习与用户先验信念框架等场景中表现优异。然而，由于依赖随机采样和蒙特卡洛估计，其样本效率有限。本文提出一种新算法——概率自然进化策略（ProbNES），通过引入贝叶斯积分改进NES框架。实验表明，ProbNES在多种任务中持续优于非概率版本及全局高效的贝叶斯优化（BO）或πBO方法，涵盖基准测试函数、数据驱动优化、用户引导的超参数调优以及运动控制任务。
原文摘要 · Abstract (English)
Zeroth-order local optimisation algorithms are essential for solving real-valued black-box optimisation problems. Among these, Natural Evolution Strategies (NES) represent a prominent class, particularly well-suited for scenarios where prior distributions are available. By optimising the objective function in the space of search distributions, NES algorithms naturally integrate prior knowledge during initialisation, making them effective in settings such as semi-supervised learning and user-prior belief frameworks. However, due to their reliance on random sampling and Monte Carlo estimates, NES algorithms can suffer from limited sample efficiency. In this paper, we introduce a novel class of algorithms, termed Probabilistic Natural Evolutionary Strategy Algorithms (ProbNES), which enhance the NES framework with Bayesian quadrature. We show that ProbNES algorithms consistently outperforms their non-probabilistic counterparts as well as global sample efficient methods such as Bayesian Optimisation (BO) or $π$BO across a wide range of tasks, including benchmark test functions, data-driven optimisation tasks, user-informed hyperparameter tuning tasks and locomotion tasks.
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