The Power of Second Chance: Personalized Submodular Maximization with Two Candidates

TL;DR

This paper introduces a personalized submodular maximization framework with two candidate solutions, enabling better customization across user-specific functions compared to traditional aggregate methods.

Contribution

It proposes a novel problem formulation for selecting two candidate sets to maximize overall utility across users, enhancing personalization in submodular maximization.

Findings

Developed algorithms for the two-candidate personalized maximization problem.

Generalized the approach to multiple candidates for increased flexibility.

Demonstrated improved personalization over aggregate methods.

Abstract

Most of existing studies on submodular maximization focus on selecting a subset of items that maximizes a \emph{single} submodular function. However, in many real-world scenarios, we might have multiple user-specific functions, each of which models the utility of a particular type of user. In these settings, our goal would be to choose a set of items that performs well across all the user-specific functions. One way to tackle this problem is to select a single subset that maximizes the sum of all of the user-specific functions. Although this aggregate approach is efficient in the sense that it avoids computation of sets for individual functions, it really misses the power of personalization - for it does not allow to choose different sets for different functions. In this paper, we introduce the problem of personalized submodular maximization with two candidate solutions. For any two candidate solutions, the utility of each user-specific function is defined as the better of these two candidates. Our objective is, therefore, to select the best set of two candidates that maximize the sum of utilities of all the user-specific functions. We have designed effective algorithms for this problem. We also discuss how our approach generalizes to multiple candidate solutions, increasing flexibility and personalization in our solution.