Common pitfalls to avoid while using multiobjective optimization in machine learning

TL;DR

This paper reviews common pitfalls in applying multiobjective optimization in machine learning, providing guidance for practitioners and illustrating issues through experiments with methods like WS, MGDA, and NSGA-II.

Contribution

It offers an entry-level guide highlighting key pitfalls and best practices for effectively applying MOO in ML, with practical examples and critical analysis.

Findings

Misinterpretation of Pareto fronts can occur without proper understanding.

Different MOO methods face unique challenges and pitfalls.

Neglecting convergence criteria can lead to misleading results.

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.