This paper presents a novel approach to multiobjective algorithms aimed at modeling the Pareto set using neural networks. Whereas previous methods mainly focused on identifying a finite number of solutions, our approach allows for the direct modeling of the entire Pareto set. Furthermore, we establish an equivalence between learning the complete Pareto set and maximizing the associated hypervolume, which enables the convergence analysis of hypervolume (as a new metric) for Pareto set learning. Specifically, our new analysis framework reveals the connection between the learned Pareto solution and its representation in a polar coordinate system. We evaluate our proposed approach on various benchmark problems and real-world problems, and the encouraging results make it a potentially viable alternative to existing multiobjective algorithms.

Theproposed algorithm first formulates a multi-task learning problem as a multiobjective optimization problem, and then decomposes the multiobjective optimization problem into a set of constrained subproblems with different trade-off preferences.

Federated learning (FL) has gain growing interests for its capability of learning from distributed data sources collectively without the need of accessing the raw data samples across different sources.

Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously. However, it is often impossible to find one single solution to optimize all the tasks, since different tasks might conflict with each other. Recently, a novel method is proposed to find one single Pareto optimal solution with good trade-off among different tasks by casting multi-task learning as multiobjective optimization. In this paper, we generalize this idea and propose a novel Pareto multi-task learning algorithm (Pareto MTL) to find a set of well-distributed Pareto solutions which can represent different trade-offs among different tasks. The proposed algorithm first formulates a multi-task learning problem as a multiobjective optimization problem, and then decomposes the multiobjective optimization problem into a set of constrained subproblems with different trade-off preferences. By solving these subproblems in parallel, Pareto MTL can find a set of well-representative Pareto optimal solutions with different trade-off among all tasks. Practitioners can easily select their preferred solution from these Pareto solutions, or use different trade-off solutions for different situations. Experimental results confirm that the proposed algorithm can generate well-representative solutions and outperform some state-of-the-art algorithms on many multi-task learning applications.

Unlike single-objective optimization, which aggregates objectives into a scalar through weighted sums, MOPs focus on generating specific or diverse Pareto solutions and learning the entire Pareto set directly.

The various clustering problems that have been studied intensively include, e.g., the

Unlike single-objective optimization, which aggregates objectives into a scalar through weighted sums, MOPs focus on generating specific or diverse Pareto solutions and learning the entire Pareto set directly.