How to Fill the Optimum Set? Population Gradient Descent with Harmless Diversity

TL;DR

This paper introduces a population gradient descent method to efficiently find a diverse set of solutions within the optimum set of a loss function, applicable to various machine learning tasks.

Contribution

It formulates the problem as a bi-level optimization to maximize diversity without compromising main loss optimization, offering a simple yet effective solution.

Findings

Successfully generates diverse solutions in multiple applications

Maintains optimization of the main loss while increasing diversity

Applicable to text-to-image, text-to-mesh, molecular, and ensemble learning

Abstract

Although traditional optimization methods focus on finding a single optimal solution, most objective functions in modern machine learning problems, especially those in deep learning, often have multiple or infinite numbers of optima. Therefore, it is useful to consider the problem of finding a set of diverse points in the optimum set of an objective function. In this work, we frame this problem as a bi-level optimization problem of maximizing a diversity score inside the optimum set of the main loss function, and solve it with a simple population gradient descent framework that iteratively updates the points to maximize the diversity score in a fashion that does not hurt the optimization of the main loss. We demonstrate that our method can efficiently generate diverse solutions on a variety of applications, including text-to-image generation, text-to-mesh generation, molecular conformation generation and ensemble neural network training.