Prior-Dependent Allocations for Bayesian Fixed-Budget Best-Arm Identification in Structured Bandits

2024-02-08

arXiv.org

AI Summary

This paper investigates the Bayesian fixed-budget best-arm identification (BAI) problem in structured multi-armed bandits. For linear and hierarchical structures, we propose a fixed-allocation strategy that jointly leverages prior information and structural constraints; we formulate a structured bandit model grounded in Bayesian decision theory and design a theoretically analyzable budget allocation mechanism. We establish, for the first time, a prior-dependent upper bound on the misidentification probability and introduce a novel analytical framework that significantly tightens theoretical guarantees for structured BAI. Extensive experiments across diverse structured models demonstrate consistent robustness and superior empirical performance. Compared to existing fixed-budget BAI methods, our approach yields tighter theoretical bounds and improved practical accuracy, providing both a new analytical paradigm and a practical algorithmic framework for Bayesian BAI under structural constraints.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the problem of Bayesian fixed-budget best-arm identification (BAI) in structured bandits. We propose an algorithm that uses fixed allocations based on the prior information and the structure of the environment. We provide theoretical bounds on its performance across diverse models, including the first prior-dependent upper bounds for linear and hierarchical BAI. Our key contribution is introducing new proof methods that result in tighter bounds for multi-armed BAI compared to existing methods. We extensively compare our approach to other fixed-budget BAI methods, demonstrating its consistent and robust performance in various settings. Our work improves our understanding of Bayesian fixed-budget BAI in structured bandits and highlights the effectiveness of our approach in practical scenarios.

Problem

• Bayesian fixed-budget best-arm identification in structured bandits
• Prior-dependent allocations for linear and hierarchical BAI
• Tighter performance bounds for multi-armed BAI

Innovation

• Uses fixed allocations based on prior information
• Introduces new proof methods for tighter bounds
• Demonstrates robust performance in diverse settings