Prior-Dependent Allocations for Bayesian Fixed-Budget Best-Arm Identification in Structured Bandits
This work addresses the problem of efficiently identifying the best arm under budget constraints in structured bandits for researchers and practitioners, representing an incremental improvement with novel theoretical bounds.
The paper tackles the problem of Bayesian fixed-budget best-arm identification in structured bandits by proposing an algorithm that uses fixed allocations based on prior information and structure, resulting in theoretical bounds including the first prior-dependent upper bounds for linear and hierarchical models and tighter bounds for multi-armed cases compared to existing methods.
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.