Robust Adaptive Submodular Maximization

07/23/2021
by   Shaojie Tang, et al.
0

Most of existing studies on adaptive submodular optimization focus on the average-case, i.e., their objective is to find a policy that maximizes the expected utility over a known distribution of realizations. However, 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 1/p+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 a cardinality constraint, 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^-1/2 under both worst case setting and average case setting simultaneously. We also describe several applications of our theoretical results, including pool-base active learning, stochastic submodular set cover and adaptive viral marketing.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/25/2022

Worst-Case Adaptive Submodular Cover

In this paper, we study the adaptive submodular cover problem under the ...
research
05/14/2019

Adaptive Robust Optimization with Nearly Submodular Structure

Constrained submodular maximization has been extensively studied in the ...
research
03/30/2016

Adaptive Maximization of Pointwise Submodular Functions With Budget Constraint

We study the worst-case adaptive optimization problem with budget constr...
research
07/04/2017

Robust Optimization for Non-Convex Objectives

We consider robust optimization problems, where the goal is to optimize ...
research
09/07/2018

Migration as Submodular Optimization

Migration presents sweeping societal challenges that have recently attra...
research
01/26/2021

Online Network Utility Maximization: Algorithm, Competitive Analysis, and Applications

We consider an online version of the well-studied network utility maximi...
research
10/12/2019

"Bring Your Own Greedy"+Max: Near-Optimal 1/2-Approximations for Submodular Knapsack

The problem of selecting a small-size representative summary of a large ...

Please sign up or login with your details

Forgot password? Click here to reset