A Finite-Sample Strong Converse for Binary Hypothesis Testing via (Reverse) Rényi Divergence
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917207098785792 |
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| author | Bruno, Roberto Vandenbroucque, Adrien Esposito, Amedeo Roberto |
| author_facet | Bruno, Roberto Vandenbroucque, Adrien Esposito, Amedeo Roberto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Finite-Sample Strong Converse for Binary Hypothesis Testing via (Reverse) Rényi Divergence Bruno, Roberto Vandenbroucque, Adrien Esposito, Amedeo Roberto Information Theory 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. |
| title | A Finite-Sample Strong Converse for Binary Hypothesis Testing via (Reverse) Rényi Divergence |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.09550 |