Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow
This addresses the problem of optimizing conflicting objectives in applications like engineering and AI, offering a novel method for handling complex Pareto fronts, though it is incremental as it builds on existing particle-based approaches.
The paper tackles multi-objective optimization by introducing an interacting particle method that combines overdamped Langevin and birth-death dynamics with a dominance potential, achieving superior performance over state-of-the-art methods on synthetic and real-world datasets.
Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach combines overdamped Langevin and birth-death dynamics, incorporating a "dominance potential" to steer particles toward global Pareto optimality. In contrast to previous methods, our method is able to relocate dominated particles, making it particularly adept at managing Pareto fronts of complicated geometries. Our method is also theoretically grounded as a Wasserstein-Fisher-Rao gradient flow with convergence guarantees. Extensive experiments confirm that our approach outperforms state-of-the-art methods on challenging synthetic and real-world datasets.