Introduction to the Analysis of Probabilistic Decision-Making Algorithms

2025-08-29

AI Summary

To address the challenge that non-experts face in understanding the theoretical foundations of probabilistic decision-making algorithms, this paper proposes a self-contained, accessible unified theoretical analysis framework covering core algorithms including multi-armed bandits, Bayesian optimization, and tree search. Methodologically, it integrates adaptive information acquisition mechanisms within a rigorous foundation of probability theory, statistics, and Gaussian process theory to model optimal decision-making under uncertainty. Its key contribution lies in the first unified, interpretable, and reusable formulation of fundamental theoretical guarantees—such as convergence rates, sample complexity bounds, and regret bounds—across these algorithmic paradigms. This framework substantially lowers the theoretical barrier for cross-domain researchers (e.g., in materials science and drug discovery), enhances algorithmic transparency and data efficiency, and provides a principled foundation for designing next-generation intelligent decision-making algorithms in high-cost experimental settings.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Online Learning & Bandits

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Providing accessible theoretical analysis of probabilistic decision-making algorithms
• Explaining behavior of bandit algorithms, Bayesian optimization, and tree search
• Making theoretical analyses understandable for non-experts in decision theory

Innovation

• Introducing theoretical analysis of probabilistic algorithms
• Covering bandit algorithms and Bayesian optimization
• Assuming basic probability and Gaussian processes knowledge