Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art

TL;DR

This survey provides a comprehensive taxonomy and state-of-the-art overview of multi-objective deep learning across supervised, unsupervised/self-supervised, generative, NAS, and reinforcement-learning paradigms. It highlights core gradient-based methods (notably MGDA), scalarization, and MOEAs, discussing their applicability, trade-offs, and computational costs in deep networks. The paper also surveys practical applications (language, vision, engineering, physics-informed ML) and discusses MORL, including single- and multi-policy strategies, as well as DL-driven MO optimization tools like surrogates. The work emphasizes that while MGDA remains central for DL, interactive, scalable, and benchmark-driven progress is needed, particularly for high-dimensional models and non-convex fronts. Overall, it positions multi-objective optimization as a growing, essential paradigm for robust, efficient, and capable deep learning systems.

Abstract

Simultaneously considering multiple objectives in machine learning has been a popular approach for several decades, with various benefits for multi-task learning, the consideration of secondary goals such as sparsity, or multicriteria hyperparameter tuning. However - as multi-objective optimization is significantly more costly than single-objective optimization - the recent focus on deep learning architectures poses considerable additional challenges due to the very large number of parameters, strong nonlinearities and stochasticity. This survey covers recent advancements in the area of multi-objective deep learning. We introduce a taxonomy of existing methods - based on the type of training algorithm as well as the decision maker's needs - before listing recent advancements, and also successful applications. All three main learning paradigms supervised learning, unsupervised learning and reinforcement learning are covered, and we also address the recently very popular area of generative modeling.

Figures (8)

• Figure 1: Left: Example of a convex Pareto front, where each point has a unique tangent, i.e., weighting vector $w^{(i)}$. Middle: Non-convex front, where multiple points have the same tangent vector. Right: Non-conflicting objectives such that the Pareto front collapses.
• Figure 2: $\ell_1$ norm and ReLU activation function for $\theta\in\mathbb{R}$.
• Figure 3: Sketch of different multiobjective optimization concepts. Entire front $\mathcal{P}_{\mathcal{F}}$ via hypervolume maximization (circles) or single point via gradient descent (squares) or preference vector scalarization (triangles).
• Figure 4: MOEA example, where a population of individuals is improved from one generation to the next ($\blacksquare\rightarrow\bigcirc\rightarrow\triangle\rightarrow\square$).
• Figure 5: Continuation algorithms use predictor steps $\widetilde{\theta}$ along the tangent space of $\mathcal{P}_c$, i.e., in parameter space (left). A corrector step then produces the next Pareto optimal point. The right plot shows the corresponding points in the objective space.

Theorems & Definitions (6)

• Remark 1
• Remark 2: Lipschitz continuous loss functions
• Remark 3: Box coverings
• Remark 4
• Remark 5: Special role of reinforcement learning
• Remark 6: A note on overparametrization