This work investigates binary hypothesis testing between $H_0\sim P_0$ and $H_1\sim P_1$ in the finite-sample regime under asymmetric error constraints. By employing the ``reverse" Rényi divergence, we derive novel non-asymptotic bounds on the Type II error probability which naturally establish a strong converse result. Furthermore, when the Type I error is constrained to decay exponentially with a rate $c$, we show that the Type II error converges to 1 exponentially fast if $c$ exceeds the Kullback-Leibler divergence $D(P_1\|P_0)$, and vanishes exponentially fast if $c$ is smaller. Finally, we present numerical examples demonstrating that the proposed converse bounds strictly improve upon existing finite-sample results in the literature.

翻译：本研究在非对称误差约束下，针对有限样本区域中的二元假设检验问题（$H_0\sim P_0$ 与 $H_1\sim P_1$）展开探讨。通过运用“反向”Rényi 散度，我们推导出关于第二类错误概率的新的非渐近界，这些界自然导出了一个强逆定理。此外，当第一类误差被约束以速率 $c$ 指数衰减时，我们证明：若 $c$ 超过 Kullback-Leibler 散度 $D(P_1\|P_0)$，则第二类误差将以指数速度收敛至 1；若 $c$ 小于该散度，则第二类误差将以指数速度趋近于零。最后，我们通过数值算例表明，所提出的逆界严格改进了现有文献中的有限样本结果。