A Simple Bound for Resilient Submodular Maximization with Curvature

TL;DR

This paper presents a theoretical bound for resilient submodular maximization that leverages curvature to improve solution quality, especially when selecting bait elements for adversarial scenarios.

Contribution

It introduces a new theoretical bound for resilient submodular maximization by applying curvature-based bait element selection to the entire solution.

Findings

Applying bait element selection to the entire solution improves theoretical guarantees.

The method enhances robustness against adversarial removals in submodular maximization.

The approach is grounded in theoretical analysis of curvature properties.

Abstract

Resilient submodular maximization refers to the combinatorial problems studied by Nemhauser and Fisher and asks how to maximize an objective given a number of adversarial removals. For example, one application of this problem is multi-robot sensor planning with adversarial attacks. However, more general applications of submodular maximization are also relevant. Tzoumas et al. obtain near-optimal solutions to this problem by taking advantage of a property called curvature to produce a mechanism which makes certain bait elements interchangeable with other elements of the solution that are produced via typical greedy means. This document demonstrates that -- at least in theory -- applying the method for selection of bait elements to the entire solution can improve that guarantee on solution quality.