Robust Maximization of Non-Submodular Objectives

20 Feb 2018  ·  Ilija Bogunovic, Junyao Zhao, Volkan Cevher ·

We study the problem of maximizing a monotone set function subject to a cardinality constraint $k$ in the setting where some number of elements $\tau$ is deleted from the returned set. The focus of this work is on the worst-case adversarial setting... While there exist constant-factor guarantees when the function is submodular, there are no guarantees for non-submodular objectives. In this work, we present a new algorithm Oblivious-Greedy and prove the first constant-factor approximation guarantees for a wider class of non-submodular objectives. The obtained theoretical bounds are the first constant-factor bounds that also hold in the linear regime, i.e. when the number of deletions $\tau$ is linear in $k$. Our bounds depend on established parameters such as the submodularity ratio and some novel ones such as the inverse curvature. We bound these parameters for two important objectives including support selection and variance reduction. Finally, we numerically demonstrate the robust performance of Oblivious-Greedy for these two objectives on various datasets. read more

PDF Abstract
No code implementations yet. Submit your code now

Tasks


Datasets


Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here