用谱表示建模图结构，实现高效全局优化。
Global Optimization on Graph-Structured Data via Gaussian Processes with Spectral Representations
- 基于低秩谱表示构建图的高斯过程代理模型。
- 在稀疏观测下仍能快速收敛，优于已有方法。
- 适合数据稀缺的图优化任务，如药物设计。
贝叶斯优化（BO）是优化昂贵黑盒目标的强大框架，但将其扩展到图结构域仍具挑战，因图具有离散和组合特性。现有方法通常依赖完整图拓扑（对大规模或部分观测图不适用）或增量探索（导致收敛缓慢）。本文提出一种可扩展的图上全局优化框架，利用低秩谱表示从稀疏结构观测中构建高斯过程（GP）代理模型。该方法通过可学习嵌入联合推断图结构与节点表示，即使在数据有限的情况下也能实现高效的全局搜索和合理的不确定性估计。我们还提供了理论分析，揭示了在不同采样策略下准确恢复底层图结构的条件。在合成与真实数据集上的实验表明，该方法相比以往方法实现了更快的收敛速度和更优的优化性能。
原文摘要 · Abstract (English)
Bayesian optimization (BO) is a powerful framework for optimizing expensive black-box objectives, yet extending it to graph-structured domains remains challenging due to the discrete and combinatorial nature of graphs. Existing approaches often rely on either full graph topology-impractical for large or partially observed graphs-or incremental exploration, which can lead to slow convergence. We introduce a scalable framework for global optimization over graphs that employs low-rank spectral representations to build Gaussian process (GP) surrogates from sparse structural observations. The method jointly infers graph structure and node representations through learnable embeddings, enabling efficient global search and principled uncertainty estimation even with limited data. We also provide theoretical analysis establishing conditions for accurate recovery of underlying graph structure under different sampling regimes. Experiments on synthetic and real-world datasets demonstrate that our approach achieves faster convergence and improved optimization performance compared to prior methods.
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