手把手讲解概率决策算法的理论分析，适合非专家入门。
Introduction to the Analysis of Probabilistic Decision-Making Algorithms
- 用基础概率与统计知识，系统解析常见决策算法原理。
- 涵盖强化学习中的贝叶斯优化、多臂赌博机等核心方法。
- 适合科研人员、工程师快速掌握算法背后的数学逻辑。
决策理论为应对各类不确定性提供了严谨的决策方法。基于这些理论的算法已在材料发现、药物研发等实际问题中取得成功应用，因其能自适应地收集信息以提升后续决策质量，从而实现高效的数据利用。在实验成本高昂的科学发现领域，这类算法可显著降低实验开销。对算法进行理论分析对于理解其行为、指导下一代算法设计至关重要。然而，现有文献中的理论分析往往对非专家不友好。本专著旨在提供一个可自包含、易于理解的入门指南，介绍多臂赌博机、贝叶斯优化和树搜索等常用概率决策算法的理论分析。仅需基础的概率论与统计学知识，以及对高斯过程的初步了解即可阅读。
原文摘要 · Abstract (English)
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug discovery. Indeed, they are desirable since they can adaptively gather information to make better decisions in the future, resulting in data-efficient workflows. In scientific discovery, where experiments are costly, these algorithms can thus significantly reduce the cost of experimentation. Theoretical analyses of these algorithms are crucial for understanding their behavior and providing valuable insights for developing next-generation algorithms. However, theoretical analyses in the literature are often inaccessible to non-experts. This monograph aims to provide an accessible, self-contained introduction to the theoretical analysis of commonly used probabilistic decision-making algorithms, including bandit algorithms, Bayesian optimization, and tree search algorithms. Only basic knowledge of probability theory and statistics, along with some elementary knowledge about Gaussian processes, is assumed.
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