Voronoi-grid-based Pareto Front Learning and Its Application to Collaborative Federated Learning

2025-05-27

AI Summary

To address incomplete Pareto front coverage and difficulties in high-dimensional ray sampling in multi-objective optimization (MOO), this paper proposes PHN-HVVS: a novel framework that replaces conventional ray-based sampling with a Voronoi mesh-driven spatial partitioning strategy. It integrates hypernetwork modeling with genetic algorithm optimization and introduces an hypervolume (HV)-guided loss function to significantly improve front coverage and convexity adaptability. The method incorporates a multi-objective cooperative federated learning architecture. Empirical evaluation on multiple MOO benchmarks demonstrates substantial improvements in Pareto set quality—measured by HV, IGD, and other standard metrics—over state-of-the-art methods. Furthermore, PHN-HVVS is validated in a collaborative federated learning setting, where it effectively balances model personalization and global fairness.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Learning & Optimization for CV
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Multi-objective optimization (MOO) exists extensively in machine learning, and aims to find a set of Pareto-optimal solutions, called the Pareto front, e.g., it is fundamental for multiple avenues of research in federated learning (FL). Pareto-Front Learning (PFL) is a powerful method implemented using Hypernetworks (PHNs) to approximate the Pareto front. This method enables the acquisition of a mapping function from a given preference vector to the solutions on the Pareto front. However, most existing PFL approaches still face two challenges: (a) sampling rays in high-dimensional spaces; (b) failing to cover the entire Pareto Front which has a convex shape. Here, we introduce a novel PFL framework, called as PHN-HVVS, which decomposes the design space into Voronoi grids and deploys a genetic algorithm (GA) for Voronoi grid partitioning within high-dimensional space. We put forward a new loss function, which effectively contributes to more extensive coverage of the resultant Pareto front and maximizes the HV Indicator. Experimental results on multiple MOO machine learning tasks demonstrate that PHN-HVVS outperforms the baselines significantly in generating Pareto front. Also, we illustrate that PHN-HVVS advances the methodologies of several recent problems in the FL field. The code is available at https://github.com/buptcmm/phnhvvs}{https://github.com/buptcmm/phnhvvs.

Problem

• Addresses challenges in Pareto-Front Learning (PFL) for multi-objective optimization.
• Improves coverage of Pareto front in high-dimensional spaces using Voronoi grids.
• Enhances federated learning by optimizing Pareto front generation with PHN-HVVS.

Innovation

• Voronoi grids decompose high-dimensional space
• Genetic algorithm optimizes Voronoi partitioning
• New loss function maximizes HV Indicator