Partial-Adaptive Submodular Maximization

TL;DR

This paper introduces a novel partial-adaptive approach for maximizing non-monotone adaptive submodular functions, balancing adaptivity benefits with reduced waiting time, applicable to constraints like cardinality and knapsack.

Contribution

It proposes the first partial-adaptive policies for non-monotone adaptive submodular maximization under various constraints, with theoretical analysis of batch query complexity.

Findings

Developed effective algorithms for partial-adaptive maximization.

Analyzed batch query complexity under certain assumptions.

Extended adaptive submodular maximization to non-monotone functions.

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 of existing studies on adaptive submodular maximization focus on the fully adaptive setting, i.e., one must wait for the feedback from \emph{all} past selections before making the next selection. Although this approach can take full advantage of feedback from the past to make informed decisions, it may take a longer time to complete the selection process as compared with the non-adaptive solution where all selections are made in advance before any observations take place. In this paper, we explore the problem of partial-adaptive submodular maximization where one is allowed to make multiple selections in a batch simultaneously and observe their realizations together. Our approach enjoys the benefits of adaptivity while reducing the time spent on waiting for the observations from past selections. To the best of our knowledge, no results are known for partial-adaptive policies for the non-monotone adaptive submodular maximization problem. We study this problem under both cardinality constraint and knapsack constraints, and develop effective and efficient solutions for both cases. We also analyze the batch query complexity, i.e., the number of batches a policy takes to complete the selection process, of our policy under some additional assumptions.