Submodular Maximization With Limited Function Access

• 成果类型: Article
• 署名作者: Downie, Andrew; Gharesifard, Bahman; Smith, Stephen L.
• 署名单位: University of Waterloo; University of California System; University of California Los Angeles
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3226713
• 发表日期: 2023
• 页码: 5522-5535
• 关键词: Autonomous systems; optimization algorithms; sensor networks; submodular maximization

摘要

In this article, we consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the objective function on sets of size two. We begin with a negative result that no algorithm using only k-wise information can guarantee performance better than k/n. We present two algorithms that utilize only pairwise information about the function and characterize their performance relative to the optimal, which depends on the curvature of the submodular function. Additionally, if the submodular function possess a property called supermodularity of conditioning, then we can provide a method to bound the performance based purely on pairwise information. The proposed algorithms offer significant computational speedups over a traditional greedy strategy. A by-product of our study is the introduction of two new notions of curvature, the $k$-Marginal Curvature and the k-Cardinality Curvature. Finally, we present experiments highlighting the performance of our proposed algorithms in terms of approximation and time complexity.