Large-scale global optimization of ultra-high dimensional non-convex landscapes based on generative neural networks

TL;DR

This paper introduces a deep generative network-based metaheuristic for efficient global optimization in ultra-high dimensional non-convex landscapes, outperforming existing methods with fewer evaluations.

Contribution

It presents a novel optimization algorithm leveraging progressive deep network growth and customized loss functions to effectively navigate high-dimensional non-convex problems.

Findings

Outperforms state-of-the-art algorithms on high-dimensional benchmarks

Requires fewer function evaluations to find high-quality solutions

Batch size for gradient sampling is independent of problem dimension

Abstract

We present a non-convex optimization algorithm metaheuristic, based on the training of a deep generative network, which enables effective searching within continuous, ultra-high dimensional landscapes. During network training, populations of sampled local gradients are utilized within a customized loss function to evolve the network output distribution function towards one peak at high-performing optima. The deep network architecture is tailored to support progressive growth over the course of training, which allows the algorithm to manage the curse of dimensionality characteristic of high-dimensional landscapes. We apply our concept to a range of standard optimization problems with dimensions as high as one thousand and show that our method performs better with fewer function evaluations compared to state-of-the-art algorithm benchmarks. We also discuss the role of deep network over-parameterization, loss function engineering, and proper network architecture selection in optimization, and why the required batch size of sampled local gradients is independent of problem dimension. These concepts form the foundation for a new class of algorithms that utilize customizable and expressive deep generative networks to solve non-convex optimization problems.