The Impact of Information in Greedy Submodular Maximization

TL;DR

This paper analyzes how limited information access among agents affects the performance of greedy algorithms in submodular maximization, providing bounds and optimal information-sharing strategies.

Contribution

It offers tight bounds on greedy algorithm performance with limited information and identifies optimal agent partitioning strategies for information sharing.

Findings

Performance degrades proportionally to the size of independent decision groups.

Optimal design partitions agents into equally-sized sets with full intra-set information.

Provides tight upper and lower bounds on solution quality based on information access.

Abstract

The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm is implemented in a distributed way, agents sequentially make decisions based on the decisions of all previous agents. This work explores how limited access to the decisions of previous agents affects the quality of the solution of the greedy algorithm. Specifically, we provide tight upper and lower bounds on how well the algorithm performs, as a function of the information available to each agent. Intuitively, the results show that performance roughly degrades proportionally to the size of the largest group of agents which make decisions independently. Additionally, we consider the case where a system designer is given a set of agents and a global limit on the amount of information that can be accessed. Our results show that the best designs partition the agents into equally-sized sets and allow agents to access the decisions of all previous agents within the same set.