Computing Approximate Pareto Frontiers for Submodular Utility and Cost Tradeoffs

TL;DR

This paper develops algorithms to compute approximate Pareto frontiers for submodular utility and cost tradeoffs, providing a comprehensive view of optimal solutions in data-mining applications.

Contribution

It introduces a formal framework and efficient algorithms for approximating the Pareto frontier in submodular utility-cost tradeoffs, moving beyond single-solution approaches.

Findings

Algorithms efficiently compute approximate Pareto frontiers.

Framework applies to diverse datasets and applications.

Provides insights into utility-cost tradeoff space.

Abstract

In many data-mining applications, including recommender systems, influence maximization, and team formation, the goal is to pick a subset of elements (e.g., items, nodes in a network, experts to perform a task) to maximize a monotone submodular utility function while simultaneously minimizing a cost function. Classical formulations model this tradeoff via cardinality or knapsack constraints, or by combining utility and cost into a single weighted objective. However, such approaches require committing to a specific tradeoff in advance and return only a single solution, offering limited insight into the space of viable utility-cost tradeoffs. In this paper, we depart from the single-solution paradigm and examine the problem of computing representative sets of high-quality solutions that expose different tradeoffs between submodular utility and cost. For this, we introduce $(\alpha_1,\alpha_2)$-approximate Pareto frontiers that provably approximate the achievable tradeoffs between submodular utility and cost. Specifically, we formalize the Pareto-$\langle f,c \rangle$ problem and develop efficient algorithms for multiple instantiations arising from different combinations of submodular utility $f$ and cost functions $c$. Our results offer a principled and practical framework for understanding and exploiting utility-cost tradeoffs in submodular optimization. Experiments on datasets from diverse application domains demonstrate that our algorithms efficiently compute approximate Pareto frontiers in practice.