Comments on the proof of adaptive submodular function minimization

TL;DR

This paper critiques a key theorem in adaptive submodular function minimization, highlighting an error that impacts the theoretical bounds in active query selection algorithms.

Contribution

It identifies a flaw in the proof of a fundamental theorem in adaptive submodularity, questioning the validity of certain expected query bounds.

Findings

An example demonstrating the incorrectness of a critical step in existing proof

Highlights the need for revised theoretical analysis in adaptive submodular optimization

Raises concerns about the reliability of current bounds in active learning algorithms

Abstract

We point out an issue with Theorem 5 appearing in "Group-based active query selection for rapid diagnosis in time-critical situations". Theorem 5 bounds the expected number of queries for a greedy algorithm to identify the class of an item within a constant factor of optimal. The Theorem is based on correctness of a result on minimization of adaptive submodular functions. We present an example that shows that a critical step in Theorem A.11 of "Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic Optimization" is incorrect.