MOGF/D: Decomposition and Cooperation in Gradient Flow for Pareto Set Learning

Gradient-based multi-objective optimization aims to construct a finite set of solutions representing diverse Pareto trade-offs, but individual gradient descent does not by itself determine how these solutions should organize as a population. Existing methods can generate multiple trade-offs through decomposition, preference adaptation, or particle interaction, but they do not explicitly separate per-subproblem descent from population-level cooperation. To address this, we propose a normal-tangent cooperation mechanism that makes population interaction gradient-orthogonal to scalar descent, which preserves first-order decrease and, after a finite formation phase, leads to an exact Lyapunov identity and conditional convergence to Pareto-critical accumulation points. Experiments on synthetic MOO benchmarks and real learning tasks show that the proposed method remains competitive on simple continuous fronts and achieves substantially larger set-quality gains on disconnected and multimodal Pareto problems.