DeepLM: Large-Scale Nonlinear Least Squares on Deep Learning Frameworks Using Stochastic Domain Decomposition

Abstract

We propose a novel approach for large-scale nonlinear least squares problems based on deep learning frameworks. Nonlinear least squares are commonly solved with the Levenberg-Marquardt (LM) algorithm for fast convergence. We implement a general and efficient LM solver on a deep learning framework by designing a new backward jacobian network to enable automatic sparse jacobian matrix computation. Furthermore, we introduce a stochastic domain decomposition approach that enables batched optimization and preserves convergence for large problems. We evaluate our method by solving bundle adjustment as a fundamental problem. Experiments show that our optimizer significantly outperforms the state-of-the-art solutions and existing deep learning solvers considering quality, efficiency, and memory. Our stochastic domain decomposition enables distributed optimization, consumes little memory and time, and achieves similar quality compared to a global solver. As a result, our solver effectively solves nonlinear least squares on an extremely large scale. We will make the code publicly available on publication.