贝叶斯优化
第三部分：贝叶斯优化
EN

贝叶斯优化

有了能够刻画自身不确定性的代理模型，优化便成为一系列决策：根据迄今为止的全部观测，代价高昂的下一次评估应当安排在何处？本部分构建做出这些决策的循环，推导这一问题的几种经典解答，并讨论如何判断优化器的优劣。

本部分的核心是采集函数：改进概率、期望改进、上置信界、Thompson 采样、知识梯度与熵搜索，分别从不同角度回答“下一次观测值多少？”。遗憾与赌博机为理论分析提供了基本术语。最后两章由教科书内容转向实践，讨论噪声、批量、约束、高维与软件，以及贝叶斯优化已取得成效的领域。

本部分假定读者已熟悉高斯过程回归（第 8 章）。

本部分各章

  1. 11 贝叶斯优化循环

    贝叶斯优化所要解决的问题；求解它的循环（拟合代理模型、最大化采集函数、评估、更新）；每个采集函数都必须做出的探索与利用的权衡；初始点的选取；这一方法的由来。

  2. 12 采集函数

    改进概率、期望改进、上置信界、Thompson 采样、知识梯度与熵搜索分别从不同角度回答“下一次评估值多少？”。本章逐一推导这些采集函数，在一维和二维中基于同一后验比较它们的行为，最后讨论定义域维度较高时如何最大化采集函数本身。

  3. 13 遗憾、赌博机与理论保证

    优化器的评分方法：简单遗憾与累积遗憾、多臂赌博机及其经典算法、Lai-Robbins 下界、基于最大信息增益的 GP-UCB 遗憾界，以及这类保证在实践中的意义与局限。

  4. 14 贝叶斯优化实践

    实际运行的贝叶斯优化系统在教科书式循环之外需要做出的决定：代理模型的设置、有噪声时报告什么、批量的选择、约束与安全、多目标、高维、成本与停止，以及各软件实现了哪些功能。

  5. 15 贝叶斯优化的用武之地

    超参数、实验室、机器人、工程设计、在线实验与人：贝叶斯优化在哪些领域取得了成效及其原因，以及它与主动学习、实验设计、赌博机、强化学习、进化策略等相邻方法的关系。

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