GRAPE提升高维黑箱优化效率,让每次查询都更接近最优解。
GRAPE: Gradient Refinement and Progress-Aware Exploitation for Query-Efficient High-Dimensional Bayesian Optimization
- 先用闭式获取函数锐化局部梯度后验,再选期望下降量大的方向更新。
- 在对抗攻击中比基线快5.4倍,在大模型提示优化中减少3.8个对数单位的遗憾。
- 适合高维、昂贵函数优化场景,尤其擅长节省查询次数。
高维黑箱函数的高效优化仍是现代机器学习与科学发现的核心挑战。尽管局部贝叶斯优化缓解了维度灾难,现有方法常优先考虑下降概率而非进步幅度,导致步长过于保守,提升微弱,浪费查询于几乎必然下降但收益极低的方向。本文提出梯度锐化与进展感知利用(GRAPE)框架,分两阶段进行:首先通过闭式采集函数锐化局部梯度后验分布,其次以条件期望下降最大为准则选择更新方向。理论分析表明,该梯度锐化阶段单调降低局部不确定性,且进展感知方向随后验变尖收敛至真实最速下降方向。实验显示,GRAPE在高维任务中展现卓越查询效率:在黑箱对抗攻击中平均提速5.4倍;在大语言模型提示优化任务中,最终平均遗憾降低3.8个对数单位,优于次优方法。
原文摘要 · Abstract (English)
Optimizing expensive, high-dimensional black-box functions remains a central challenge in modern machine learning and scientific discovery. While local Bayesian optimization mitigates the curse of dimensionality, existing techniques often prioritize the probability of descent over the magnitude of progress. This leads to overly conservative steps that yield negligible improvement, wasting queries on directions that are nearly certain to descend but offer little decrease. We introduce Gradient Refinement and Progress-Aware Exploitation (GRAPE), a two-stage framework that first sharpens the local gradient posterior via a closed-form acquisition function, then selects update directions by maximizing the expected decrease conditional on descent. Theoretical analysis proves that this gradient refinement stage monotonically minimizes local uncertainty and that the progress-aware direction converges to true steepest descent as the posterior sharpens. Empirically, GRAPE demonstrates superior query efficiency across high-dimensional tasks: in black-box adversarial attacks, it achieves an average 5.4$\times$ speedup over baselines, and on large language model prompt optimization tasks, it outperforms the second best method by a reduction of 3.8 log-units in the final average regret.
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