Multi-Fidelity Multi-Armed Bandits Revisited

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

Bibtex Paper Supplemental


Xuchuang Wang, Qingyun Wu, Wei Chen, John C.S. Lui


We study the multi-fidelity multi-armed bandit ($\texttt{MF-MAB}$), an extension of the canonical multi-armed bandit (MAB) problem.$\texttt{MF-MAB}$ allows each arm to be pulled with different costs (fidelities) and observation accuracy.We study both the best arm identification with fixed confidence ($\texttt{BAI}$) and the regret minimization objectives.For $\texttt{BAI}$, we present (a) a cost complexity lower bound, (b) an algorithmic framework with two alternative fidelity selection procedures,and (c) both procedures' cost complexity upper bounds.From both cost complexity bounds of $\texttt{MF-MAB}$,one can recover the standard sample complexity bounds of the classic (single-fidelity) MAB.For regret minimization of $\texttt{MF-MAB}$, we propose a new regret definition, prove its problem-independent regret lower bound $\Omega(K^{1/3}\Lambda^{2/3})$ and problem-dependent lower bound $\Omega(K\log \Lambda)$, where $K$ is the number of arms and $\Lambda$ is the decision budget in terms of cost, and devise an elimination-based algorithm whose worst-cost regret upper bound matches its corresponding lower bound up to some logarithmic terms and, whose problem-dependent bound matches its corresponding lower bound in terms of $\Lambda$.