Beyond Adaptive Submodularity: Approximation Guarantees of Greedy Policy with Adaptive Submodularity Ratio
This work addresses a theoretical gap for researchers in optimization and machine learning, providing new guarantees for practical greedy methods in sequential decision-making, though it is incremental in extending existing submodularity concepts.
The authors tackled the limited theoretical understanding of greedy policies in adaptive stochastic optimization by introducing the adaptive submodularity ratio, which enabled proving approximation guarantees for a broader class of problems, including adaptive influence maximization and adaptive feature selection, with experiments showing competitive performance against standard heuristics.
We propose a new concept named adaptive submodularity ratio to study the greedy policy for sequential decision making. While the greedy policy is known to perform well for a wide variety of adaptive stochastic optimization problems in practice, its theoretical properties have been analyzed only for a limited class of problems. We narrow the gap between theory and practice by using adaptive submodularity ratio, which enables us to prove approximation guarantees of the greedy policy for a substantially wider class of problems. Examples of newly analyzed problems include important applications such as adaptive influence maximization and adaptive feature selection. Our adaptive submodularity ratio also provides bounds of adaptivity gaps. Experiments confirm that the greedy policy performs well with the applications being considered compared to standard heuristics.