提出NVA方法，高效搜索非凸优化中的多个极值点。
Natural Variational Annealing for Multimodal Optimization
- 用高斯混合分布同时探索多极值点
- 通过退火策略逐步平衡探索与利用
- 结合进化算法的适应度塑造，适合复杂优化场景
我们提出一种名为自然变分退火（Natural Variational Annealing, NVA）的新多模态优化方法，融合变分后验、退火机制和自然梯度学习三大核心思想，用于同时寻找黑箱非凸目标函数的多个全局及局部极值。该方法采用高斯混合分布实现并行搜索，通过退火策略渐进地从探索转向利用，并利用自然梯度学习更新变分分布，其更新形式类似易实现的经典算法。三者结合使NVA能引入进化算法中的“适应度塑造”机制。我们在模拟实验中评估了搜索质量，并与基于梯度下降和进化策略的方法进行对比。此外，还将其应用于行星科学中的一个真实逆问题。
原文摘要 · Abstract (English)
We introduce a new multimodal optimization approach called Natural Variational Annealing (NVA) that combines the strengths of three foundational concepts to simultaneously search for multiple global and local modes of black-box nonconvex objectives. First, it implements a simultaneous search by using variational posteriors, such as, mixtures of Gaussians. Second, it applies annealing to gradually trade off exploration for exploitation. Finally, it learns the variational search distribution using natural-gradient learning where updates resemble well-known and easy-to-implement algorithms. The three concepts come together in NVA giving rise to new algorithms and also allowing us to incorporate "fitness shaping", a core concept from evolutionary algorithms. We assess the quality of search on simulations and compare them to methods using gradient descent and evolution strategies. We also provide an application to a real-world inverse problem in planetary science.
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