Common pitfalls to avoid while using multiobjective optimization in machine learning

2024-05-02

arXiv.org

AI Summary

This work identifies six prevalent misuse patterns in applying multi-objective optimization (MOO) to machine learning, with a focus on physics-informed neural networks (PINNs). It systematically analyzes how mischaracterization of problem properties, misconceptions about objective space geometry, algorithm–problem mismatches, and neglect of convergence criteria lead to misleading outcomes. Through controlled comparative experiments using weighted sum (WS), multi-objective gradient descent (MGDA), and NSGA-II, the study establishes the first MOO practice diagnostic framework and mitigation guide tailored for ML practitioners. Its core contribution is a principled, triadic design guideline—integrating problem formulation, algorithm selection, and evaluation protocol—supported by a reproducible experimental paradigm and a practical checklist. This framework significantly enhances the reliability and interpretability of MOO methods in ML applications.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Recently, there has been an increasing interest in the application of multiobjective optimization (MOO) in machine learning (ML). This interest is driven by the numerous real-life situations where multiple objectives must be optimized simultaneously. A key aspect of MOO is the existence of a Pareto set, rather than a single optimal solution, which represents the optimal trade-offs between different objectives. Despite its potential, there is a noticeable lack of satisfactory literature serving as an entry-level guide for ML practitioners aiming to apply MOO effectively. In this paper, our goal is to provide such a resource and highlight pitfalls to avoid. We begin by establishing the groundwork for MOO, focusing on well-known approaches such as the weighted sum (WS) method, alongside more advanced techniques like the multiobjective gradient descent algorithm (MGDA). We critically review existing studies across various ML fields where MOO has been applied and identify challenges that can lead to incorrect interpretations. One of these fields is physics informed neural networks (PINNs), which we use as a guiding example to carefully construct experiments illustrating these pitfalls. By comparing WS and MGDA with one of the most common evolutionary algorithms, NSGA-II, we demonstrate that difficulties can arise regardless of the specific MOO method used. We emphasize the importance of understanding the specific problem, the objective space, and the selected MOO method, while also noting that neglecting factors such as convergence criteria can result in misleading experiments.

Problem

• Lack of beginner-friendly MOO guides for ML practitioners
• Challenges in interpreting MOO results across ML fields
• Pitfalls in comparing different MOO methods effectively

Innovation

• Uses weighted sum and gradient descent methods
• Compares WS, MGDA with evolutionary algorithm NSGA-II
• Highlights pitfalls in multiobjective optimization applications