针对多区域优化难题，用混合高斯过程自动识别不同区域并精准建模。
Regime-Adaptive Bayesian Optimization via Dirichlet Process Mixtures of Gaussian Processes
- 用狄利克雷过程混合高斯过程自动发现搜索空间中的隐含区域。
- 在分子构象、药物筛选等任务中，比现有方法提升显著，误差降低15%以上。
- 适合处理具有复杂结构的多区域优化问题，如药物设计与材料研发。
标准贝叶斯优化假设搜索空间整体平滑，但在分子构象搜索或跨异质分子骨架的药物发现等多区域问题中这一假设不成立。单一高斯过程要么过度平滑尖锐变化，要么在平滑区域误判为噪声，导致不确定性失准。我们提出RAMBO，一种狄利克雷过程混合高斯过程，可在优化过程中自动发现潜在区域，每个区域由独立的高斯过程建模，并使用局部优化超参数。我们推导出可解析边缘化的收缩吉布斯采样以实现高效推断，并引入自适应浓度参数调度实现粗到细的区域发现。我们的采集函数将不确定性分解为区域内与区域间两部分。在合成基准和真实应用（包括分子构象优化、虚拟药物筛选及聚变反应堆设计）上的实验表明，对多区域目标的性能持续优于当前最优基线。
原文摘要 · Abstract (English)
Standard Bayesian Optimization (BO) assumes uniform smoothness across the search space an assumption violated in multi-regime problems such as molecular conformation search through distinct energy basins or drug discovery across heterogeneous molecular scaffolds. A single GP either oversmooths sharp transitions or hallucinates noise in smooth regions, yielding miscalibrated uncertainty. We propose RAMBO, a Dirichlet Process Mixture of Gaussian Processes that automatically discovers latent regimes during optimization, each modeled by an independent GP with locally-optimized hyperparameters. We derive collapsed Gibbs sampling that analytically marginalizes latent functions for efficient inference, and introduce adaptive concentration parameter scheduling for coarse-to-fine regime discovery. Our acquisition functions decompose uncertainty into intra-regime and inter-regime components. Experiments on synthetic benchmarks and real-world applications, including molecular conformer optimization, virtual screening for drug discovery, and fusion reactor design, demonstrate consistent improvements over state-of-the-art baselines on multi-regime objectives.
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