Analysis of Multitasking Pareto Optimization for Monotone Submodular Problems

2026-04-16

AI Summary

This work addresses the optimization of multiple tasks that share identical monotone submodular objective functions but are subject to distinct knapsack constraints. The authors propose a multi-task Pareto optimization approach that jointly solves all tasks in a single run. By integrating multi-task learning into the Pareto optimization framework for the first time, the method leverages a shared population to facilitate solution transfer across tasks and introduces a novel mechanism to generate compact Pareto fronts, thereby enhancing computational efficiency. Theoretical analysis establishes that the algorithm achieves a (1−1/e)-approximation guarantee for each task within expected polynomial runtime. Empirical results demonstrate significant performance gains over independent optimization baselines when element costs are uniform, while also revealing limitations under heterogeneous cost settings.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately. We introduce multitasking formulations of these problems that are an effective way to solve multiple related problems with a single run. In our setting the given problems share a monotone submodular function $f$ but have different knapsack constraints. We examine the case where elements within a constraint have the same cost and show that our multitasking formulations result in small Pareto fronts. This allows the population to share solutions between all problems leading to significant improvements compared to running several classical approaches independently. Using rigorous runtime analysis, we analyze the expected time until the introduced multitasking approaches obtain a $(1-1/e)$-approximation for each of the given problems. Our experimental investigations for the maximum coverage problem give further insight into the dynamics behind how the approach works and doesn't work in practice for problems where elements within a constraint also have varied costs.

Problem

• multitasking
• Pareto optimization
• monotone submodular
• knapsack constraints
• multi-objective optimization

Innovation

• multitasking optimization
• Pareto optimization
• monotone submodular functions
• evolutionary multi-objective algorithms
• knapsack constraints