Sharp Non-Asymptotic Analysis of the Penalized Challenger in $\beta$-EB-TCI for Bernoulli Bandits

תקציר מקורי באנגליתarXiv:2610.01951v1 Announce Type: new Abstract: Top-two algorithms are simple and effective for fixed-confidence best-arm identification, but their sharp non-asymptotic behavior is still not well understood. We study this problem for Bernoulli bandits through $\beta$-EB-TCI, the empirical-best top-two rule of Jourdan et al., whose challenger is chosen using a Bernoulli transportation cost with a logarithmic count penalty. We prove that, after the empirical leader has become the true best arm and its sampling fraction stays close to $\beta$, the stopping time is $T_{\beta}^{\star}(\mu)\log(1/\delta)$ up to lower-order concentration terms. We also show that, in this regime, every challenger is sampled linearly often. Thus, for the original algorithm without forced exploration, the main remai