Structured Robust Submodular Maximization: Offline and Online Algorithms

TL;DR

This paper introduces efficient algorithms with provable guarantees for robust submodular maximization under structured constraints, applicable in offline and online settings, improving stability and modeling scope in subset selection problems.

Contribution

It presents novel algorithms for robust submodular maximization with structured constraints, extending classical methods to offline and online scenarios with theoretical guarantees.

Findings

Provides a nearly optimal bi-criteria approximation algorithm for offline problems.

Develops an online algorithm with sub-linear regret for dynamic data.

Extends classical submodular maximization algorithms to robust, structured settings.

Abstract

Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions obtained via this approach are unstable to perturbations in data defining the submodular functions. Robust submodular maximization has been proposed as a richer model that aims to overcome this discrepancy as well as increase the modeling scope of submodular optimization. In this work, we consider robust submodular maximization with structured combinatorial constraints and give efficient algorithms with provable guarantees. Our approach is applicable to constraints defined by single or multiple matroids, knapsack as well as distributionally robust criteria. We consider both the offline setting where the data defining the problem is known in advance as well as the online setting where the input data is revealed over time. For the offline setting, we give a general (nearly) optimal bi-criteria approximation algorithm that relies on new extensions of classical algorithms for submodular maximization. For the online version of the problem, we give an algorithm that returns a bi-criteria solution with sub-linear regret.