Title: Fixed Budget Complexity is Comparable to Fixed Confidence in Best-Arm Identification Within Logarithmic Bounds

Abstract: Best-arm identification (BAI) stands as a cornerstone challenge in interactive machine learning, manifesting in two primary variations: the fixed-budget (FB) and fixed-confidence (FC) frameworks. For standard K-armed bandits featuring a distinct optimal arm, the theoretical sample complexities for both regimes are well-established and converge up to logarithmic terms. This equivalence raises a pivotal question regarding more general, potentially structured BAI scenarios: does one setting impose greater difficulty than the other? This study demonstrates that, within logarithmic factors, the fixed-budget problem is not more challenging than the fixed-confidence problem. We provide a constructive proof via FC2FB, a novel meta-algorithm designed to convert any FC algorithm $\mathcal{A}$ into an FB counterpart. We establish that the sample complexity of FC2FB aligns with that of $\mathcal{A}$ up to logarithmic factors, thereby positioning the optimal FC sample complexity as an upper bound for the optimal FB sample complexity within this margin. Beyond elucidating the intrinsic connection between FB and FC, our findings offer practical utility: integrating FC2FB with current state-of-the-art FC algorithms yields enhanced sample complexity performance across various FB problem instances.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC