Resilient Monotone Submodular Function Maximization
For practitioners in machine learning, optimization, and control requiring resilient selection, this work offers a scalable algorithm with theoretical guarantees, though the improvement is incremental over existing non-resilient methods.
The paper addresses resilient selection of elements (e.g., features, sensors) against adversarial attacks or failures, where the objective is monotone submodular. It provides the first scalable, curvature-dependent algorithm for approximate solution, valid for any number of attacks, achieving superior approximation for low-curvature functions.
In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or failures. In general, such resilient optimization problems are hard, and cannot be solved exactly in polynomial time, even though they often involve objective functions that are monotone and submodular. Notwithstanding, in this paper we provide the first scalable, curvature-dependent algorithm for their approximate solution, that is valid for any number of attacks or failures, and which, for functions with low curvature, guarantees superior approximation performance. Notably, the curvature has been known to tighten approximations for several non-resilient maximization problems, yet its effect on resilient maximization had hitherto been unknown. We complement our theoretical analyses with supporting empirical evaluations.