# Robust Adaptive Submodular Maximization

arXiv: https://arxiv.org/abs/2107.11333 · HTML: https://mlsanity.com/paper/2107.11333/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 23 Jul 2021.

## Builds on (most cited first, 9 of 9)

- [Lazier Than Lazy Greedy](https://mlsanity.com/paper/1409.7938/) (2014)
- [Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint](https://mlsanity.com/paper/2007.05014/) (2020)
- [Beyond Pointwise Submodularity: Non-Monotone Adaptive Submodular Maximization in Linear Time](https://mlsanity.com/paper/2008.05004/) (2020)
- [Optimal Sampling Gaps for Adaptive Submodular Maximization](https://mlsanity.com/paper/2104.01750/) (2021)
- [Adaptive Regularized Submodular Maximization](https://mlsanity.com/paper/2103.00384/) (2021)
- [Beyond Pointwise Submodularity: Non-Monotone Adaptive Submodular Maximization subject to Knapsack and k-System Constraints](https://mlsanity.com/paper/2104.04853/) (2021)
- [No Time to Observe: Adaptive Influence Maximization with Partial Feedback](https://mlsanity.com/paper/1609.00427/) (2016)
- [Stochastic Submodular Cover with Limited Adaptivity](https://mlsanity.com/paper/1810.13351/) (2018)
- [Towards Nearly-linear Time Algorithms for Submodular Maximization with a Matroid Constraint](https://mlsanity.com/paper/1811.07464/) (2018)

## Built on by (most cited first, 4 of 4)

- [Partial-Monotone Adaptive Submodular Maximization](https://mlsanity.com/paper/2207.12840/) (2022)
- [Streaming Adaptive Submodular Maximization](https://mlsanity.com/paper/2208.08021/) (2022)
- [Worst-Case Adaptive Submodular Cover](https://mlsanity.com/paper/2210.13694/) (2022)
- [Adaptive Combinatorial Maximization: Beyond Approximate Greedy Policies](https://mlsanity.com/paper/2404.01930/) (2024)

## Abstract (arXiv)

The goal of a sequential decision making problem is to design an interactive policy that adaptively selects a group of items, each selection is based on the feedback from the past, in order to maximize the expected utility of selected items. It has been shown that the utility functions of many real-world applications are adaptive submodular. However, most of existing studies on adaptive submodular optimization focus on the average-case. Unfortunately, a policy that has a good average-case performance may have very poor performance under the worst-case realization. In this study, we propose to study two variants of adaptive submodular optimization problems, namely, worst-case adaptive submodular maximization and robust submodular maximization. The first problem aims to find a policy that maximizes the worst-case utility and the latter one aims to find a policy, if any, that achieves both near optimal average-case utility and worst-case utility simultaneously. We introduce a new class of stochastic functions, called worst-case submodular function. For the worst-case adaptive submodular maximization problem subject to a p-system constraint, we develop an adaptive worst-case greedy policy that achieves a frac1p+1 approximation ratio against the optimal worst-case utility if the utility function is worst-case submodular. For the robust adaptive submodular maximization problem subject to cardinality constraints (resp. partition matroid constraints), if the utility function is both worst-case submodular and adaptive submodular, we develop a hybrid adaptive policy that achieves an approximation close to 1-e^-frac12 (resp. 1/3) under both worst- and average-case settings simultaneously. We also describe several applications of our theoretical results, including pool-base active learning, stochastic submodular set cover and adaptive viral marketing.