PreprintCC BY-NC-SA 4.0arXiv
PDE-Based Bounds on Optimal Exponents in Active Simple Hypothesis Testing
Abstract
We present general upper and lower bounds on the optimal error exponent for the Active Simple Hypothesis Testing (ASHT) problem. ASHT has been extensively studied across diverse fields including Information Theory, Bandits, and Operations Research, a precise characterization of this optimal exponent has remained elusive. This work combines a recent Partial Differential Equation (PDE) characterization of the optimal exponent by Vijayan (2025) with the comparison principle of viscosity solutions of Hamilton-Jacobi PDEs. This leads to bounds that are parametrized by convex functions, sets and lower Hamiltonian relaxations, a flexibility that generalizes many known results in the literature.
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BibTeX
@misc{vijayan2026pdebased,
title = {{PDE-Based Bounds on Optimal Exponents in Active Simple Hypothesis Testing}},
author = {Sushant Vijayan and Himadri Mandal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36657},
eprint = {2610.36657},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36657},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - PDE-Based Bounds on Optimal Exponents in Active Simple Hypothesis Testing
AU - Sushant Vijayan
AU - Himadri Mandal
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36657
UR - https://arxiv.org/abs/2610.36657
AB - We present general upper and lower bounds on the optimal error exponent for the Active Simple Hypothesis Testing (ASHT) problem. ASHT has been extensively studied across diverse fields including Information Theory, Bandits, and Operations Research, a precise characterization of this optimal exponent has remained elusive. This work combines a recent Partial Differential Equation (PDE) characterization of the optimal exponent by Vijayan (2025) with the comparison principle of viscosity solutions of Hamilton-Jacobi PDEs. This leads to bounds that are parametrized by convex functions, sets and lower Hamiltonian relaxations, a flexibility that generalizes many known results in the literature.
ER -