提出新优化框架，可概率收敛到全局最优解。
Proximal basin hopping: global optimization with guarantees
- 融合近端优化与局部最小化，设计新型全局优化算法
- 有限采样下以高概率收敛至全局最优
- 高维场景下性能显著优于经典理论算法
全局优化问题虽有众多算法表现出色，但理论支撑不足。本文提出一种名为近端盆地跳跃（Proximal Basin Hopping, PBH）的全新理论框架，巧妙结合近端优化与局部最小化。基于该框架构建的实际算法，在使用有限样本时，可高概率收敛至全局最小值。在标准合成难函数及深度学习缩放律拟合等真实问题上，PBH均优于具有理论保障的经典算法，且维度越高，性能差距越明显。
原文摘要 · Abstract (English)
Global optimization is a challenging problem, with plenty of algorithms displaying empirical success, but scarce theoretical backing. In this work, we propose a new theoretical framework called Proximal Basin Hopping (PBH), carefully tailored to combine proximal optimization and local minimization. We use it to construct a practical algorithm that converges to the global minimizer with high probability, when using a finite amount of samples. Proximal Basin Hopping outperforms well known algorithms with theoretical backing on standard synthetic hard functions, and real problems such as fitting scaling laws for deep learning. Furthermore, the higher the dimension, the better the performance gap.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。