# Adversarially Robust Submodular Maximization under Knapsack Constraints

## TL;DR

This paper introduces the first scalable adversarially robust algorithms for monotone submodular maximization under knapsack constraints, demonstrating strong empirical performance on social network and recommendation datasets.

## Contribution

It presents novel scalable algorithms for robust submodular maximization under multiple knapsack constraints, with theoretical guarantees and practical effectiveness.

## Key findings

- Algorithms achieve near-optimal robust solutions with polylogarithmic factors.
- Strong empirical performance on social network and recommendation datasets.
- Outperforms or matches existing non-robust algorithms in robustness and objective value.

## Abstract

We propose the first adversarially robust algorithm for monotone submodular maximization under single and multiple knapsack constraints with scalable implementations in distributed and streaming settings. For a single knapsack constraint, our algorithm outputs a robust summary of almost optimal (up to polylogarithmic factors) size, from which a constant-factor approximation to the optimal solution can be constructed. For multiple knapsack constraints, our approximation is within a constant-factor of the best known non-robust solution. We evaluate the performance of our algorithms by comparison to natural robustifications of existing non-robust algorithms under two objectives: 1) dominating set for large social network graphs from Facebook and Twitter collected by the Stanford Network Analysis Project (SNAP), 2) movie recommendations on a dataset from MovieLens. Experimental results show that our algorithms give the best objective for a majority of the inputs and show strong performance even compared to offline algorithms that are given the set of removals in advance.