Year: 2026
Type: conference-paper
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.
Authors: Himadri Mandal, Sushant Vijayan
Institutions: Ashoka University, Tata Institute of Fundamental Research
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204155402