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

*Proceedings of the 39th International Conference on Machine Learning*, PMLR 162:7650-7664, 2022.

#### 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 number of optimal points. 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 multiple applications, e.g. text-to-image generation, text-to-mesh generation, molecular conformation generation and ensemble neural network training.