An Almost Optimal Algorithm for Unbounded Search with Noisy Information

Abstract

Given a sequence of integers, 𝒮 = s₁, s₂,… in ascending order, called the search domain, and an integer t, called the target, the predecessor problem asks for the target index N such that s_N is the largest integer in 𝒮 satisfying s_N ≤ t. We consider solving the predecessor problem with the least number of queries to a binary comparison oracle. For each query index i, the oracle returns whether s_i ≤ t or s_i > t. In particular, we study the predecessor problem under the UnboundedNoisy setting, where (i) the search domain 𝒮 is unbounded, i.e., n = |𝒮| is unknown or infinite, and (ii) the binary comparison oracle is noisy. We denote the former setting by Unbounded and the latter by Noisy..