The Impact of Message Passing in Agent-Based Submodular Maximization

Submodular maximization problems are a relevant model set for many real-world applications. Since these problems are generally NP-Hard, many methods have been developed to approximate the optimal solution in polynomial time. One such approach uses an agent-based greedy algorithm, where the goal is for each agent to choose an action from its action set such that the union of all actions chosen is as high-valued as possible. Recent work has shown how the performance of the greedy algorithm degrades as the amount of information shared among the agents decreases, whereas this work addresses the scenario where agents are capable of sharing more information than allowed in the greedy algorithm. Specifically, we show how performance guarantees increase as agents are capable of passing messages, which can augment the allowable decision set for each agent. Under these circumstances, we show a near-optimal method for message passing, and how much such an algorithm could increase performance for any given problem instance.

[1]  Andreas Krause,et al.  Efficient Planning of Informative Paths for Multiple Robots , 2006, IJCAI.

[2]  Nathan Michael,et al.  Distributed matroid-constrained submodular maximization for multi-robot exploration: theory and practice , 2018, Auton. Robots.

[3]  Martin Gairing,et al.  Covering Games: Approximation through Non-cooperation , 2009, WINE.

[4]  João Pedro Hespanha,et al.  Strategic Information Sharing in Greedy Submodular Maximization , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[5]  Philip N. Brown,et al.  The Cost of Denied Observation in Multiagent Submodular Optimization , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[6]  Jure Leskovec,et al.  Inferring networks of diffusion and influence , 2010, KDD.

[7]  Jason R. Marden.  The Role of Information in Distributed Resource Allocation , 2017, IEEE Transactions on Control of Network Systems.

[8]  Nathan Michael,et al.  Distributed Submodular Maximization on Partition Matroids for Planning on Large Sensor Networks , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[9]  Andreas Krause,et al.  Cost-effective outbreak detection in networks , 2007, KDD '07.

[10]  João Pedro Hespanha,et al.  Impact of information in greedy submodular maximization , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[11]  Na Li,et al.  Distributed greedy algorithm for multi-agent task assignment problem with submodular utility functions , 2019, Autom..

[12]  Bahman Gharesifard,et al.  On distributed submodular maximization with limited information , 2016, 2016 American Control Conference (ACC).

[13]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[14]  C. Guestrin,et al.  Near-optimal sensor placements: maximizing information while minimizing communication cost , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[15]  Andreas Krause,et al.  Distributed Submodular Maximization: Identifying Representative Elements in Massive Data , 2013, NIPS.

[16]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[17]  Jan Vondrák,et al.  Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract) , 2007, IPCO.

[18]  Martin Grötschel,et al.  The ellipsoid method and its consequences in combinatorial optimization , 1981, Comb..

[19]  Hui Lin,et al.  A Class of Submodular Functions for Document Summarization , 2011, ACL.

[20]  João Pedro Hespanha,et al.  Heterogeneous Measurement Selection for Vehicle Tracking using Submodular Optimization , 2019, 2020 IEEE Aerospace Conference.

[21]  Radha Poovendran,et al.  A submodular optimization framework for leader selection in linear multi-agent systems , 2011, IEEE Conference on Decision and Control and European Control Conference.