Lower Bound on the Greedy Approximation Ratio for Adaptive Submodular Cover
This addresses a theoretical gap in optimization algorithms for researchers in machine learning and operations research, but it is incremental as it corrects an existing result.
The paper shows that the greedy algorithm for adaptive-submodular cover has an approximation ratio of at least 1.3*(1+ln Q), using an instance with Q=1 to invalidate a prior claim of a (1+ln Q)^2 ratio by Golovin-Krause.
We show that the greedy algorithm for adaptive-submodular cover has approximation ratio at least 1.3*(1+ln Q). Moreover, the instance demonstrating this gap has Q=1. So, it invalidates a prior result in the paper ``Adaptive Submodularity: A New Approach to Active Learning and Stochastic Optimization'' by Golovin-Krause, that claimed a (1+ln Q)^2 approximation ratio for the same algorithm.