将贝叶斯优化与信任域方法结合，实现高效全局搜索与局部精调的自适应协同。
LAGO: A Local-Global Optimization Framework Combining Trust Region Methods and Bayesian Optimization
- 通过竞争机制分离全局探索与局部精调，分别在信任域外和内生成候选点。
- 局部更新后仅当距离满足长度尺度条件才加入全局数据集，避免数值不稳。
- 适合高成本、梯度可得的光滑函数优化，尤其擅长在优质区域快速收敛。
我们提出LAGO，一种针对平滑且评估代价高的目标函数（具备梯度信息）的局部-全局优化框架，融合贝叶斯优化（BO）与基于梯度的信任域局部精炼。每轮迭代中，全局与局部策略独立生成候选点，下一评估点根据预测改进选择。LAGO在提议阶段分离全局探索与局部精炼：BO采集函数在活跃信任域外优化，而局部候选点在信任域内生成。仅当新点与已接受的局部步长满足基于长度尺度的最小距离条件时，才将其纳入全局高斯过程数据集，从而降低局部开发中的数值不稳定性风险。LAGO在到达有潜力区域时增强局部精炼效率，并在局部步骤无竞争力时自动恢复探索行为。
原文摘要 · Abstract (English)
We introduce LAGO, a LocAl-Global Optimization framework coupling Bayesian Optimization (BO) and gradient-based trust region local refinement through an adaptive competition mechanism for smooth expensive-to-evaluate objective functions with available gradients. At each iteration, global and local optimization strategies independently propose candidate points, and the next evaluation is selected based on predicted improvement. LAGO separates global exploration from local refinement at the proposal level: the BO acquisition function is optimized outside the active trust region, while local candidates are proposed within the trust region. Points in the vicinity of the accepted local step are incorporated in the global GP dataset only when satisfying a lengthscale-based minimum-distance criterion, hence reducing the risk of numerical instability during local exploitation. LAGO enhances BO with efficient local refinement when reaching promising regions, and reverts to exploratory behavior when local steps are not competitive.
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