Computing Approximate Pareto Frontiers for Submodular Utility and Cost Tradeoffs

2026-02-17

AI Summary

This work addresses the challenge of balancing submodular utility maximization against cost minimization in applications such as recommender systems and influence maximization, where traditional approaches yield only a single solution and fail to capture the rich trade-offs between these objectives. The paper formally introduces the Pareto-⟨f,c⟩ problem and proposes the notion of an (α₁,α₂)-approximate Pareto front. It further develops efficient algorithms that provably approximate the Pareto set for diverse combinations of submodular utility and cost functions. Extensive experiments on multiple real-world datasets demonstrate that the proposed method efficiently generates high-quality approximate fronts, substantially enhancing decision-making flexibility by revealing a spectrum of viable trade-offs between utility and cost.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 $(α_1,α_2)$-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.

Problem

• submodular optimization
• Pareto frontier
• utility-cost tradeoff
• multi-objective optimization
• approximation algorithms

Innovation

• submodular optimization
• Pareto frontier
• utility-cost tradeoff
• approximation algorithm
• multi-objective optimization