A0385
Title: Multiple Wasserstein gradient descent algorithm for multi-objective distributional optimization
Authors: DaiHai Nguyen - Hokkaido University (Japan) [presenting]
Abstract: The optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions is addressed. This type of multi-objective distributional optimization commonly arises in machine learning and statistics, with applications in areas such as multiple target sampling, multi-task learning, and multi-objective generative modeling. To solve this problem, an iterative particle-based algorithm is proposed, called muliple Wasserstein gradient descent (MWGraD), which constructs a flow of intermediate empirical distributions, each being represented by a set of particles, which gradually minimize the multiple objective functionals simultaneously. Specifically, MWGraD consists of two key steps at each iteration. First, it estimates the Wasserstein gradient for each objective function based on the current particles. Then, it aggregates these gradients into a single Wasserstein gradient using dynamically adjusted weights and updates the particles accordingly. In addition, theoretical analysis is provided, and experimental results are presented on both synthetic and real-world datasets, demonstrating the effectiveness of MWGraD.
