Partial-Adaptive Submodular Maximization

Shaojie Tang, Jing Yuan

Abstract: The goal of a typical adaptive sequential decision making problem is to design an interactive policy that selects a group of items sequentially, based on some partial observations, to maximize the expected utility. It has been shown that the utility functions of many real-world applications, including pooled-based active learning and adaptive influence maximization, satisfy the property of adaptive submodularity. However, most studies on adaptive submodular maximization focus on fully adaptive settings, which can take a long time to complete. In this paper, we propose a partial-adaptive submodular maximization approach where multiple selections can be made in a batch and observed together, reducing the waiting time for observations. We develop effective and efficient solutions for both cardinality and knapsack constraints and analyzes the batch query complexity. We are the first to explore partial-adaptive policies for non-monotone adaptive submodular maximization problems.