Progressive Batching for Efficient Non-linear Least Squares

Huu Le, Christopher Zach, Edward Rosten, Oliver J. Woodford; Proceedings of the Asian Conference on Computer Vision (ACCV), 2020

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying problem structure for computational speedup. With the success of deep learning methods leveraging large datasets, stochastic optimization methods received recently a lot of attention. Our work borrows ideas from both stochastic machine learning and statistics, and we present an approach for non-linear least-squares that guarantees convergence while at the same time significantly reduces the required amount of computation. Empirical results show that our proposed method achieves competitive convergence rates compared to traditional second-order approaches on common computer vision problems such as essential/fundamental matrix estimation with very large numbers of correspondences.