Training Deep Neural Networks via Branch-and-Bound

TL;DR

This paper introduces BPGrad, an innovative branch-and-bound based algorithm for deep neural network training that adaptively determines step sizes and achieves optimal solutions efficiently, outperforming some existing stochastic methods.

Contribution

The paper presents BPGrad, a novel approximate algorithm for deep neural network training that adaptively estimates feasible regions and guarantees finite-step optimality.

Findings

BPGrad performs well in object recognition, detection, and segmentation tasks.

Empirical results show BPGrad compares favorably to other stochastic optimization methods.

The method efficiently finds optimal solutions within finite iterations.

Abstract

In this paper, we propose BPGrad, a novel approximate algorithm for deep nueral network training, based on adaptive estimates of feasible region via branch-and-bound. The method is based on the assumption of Lipschitz continuity in objective function, and as a result, it can adaptively determine the step size for the current gradient given the history of previous updates. We prove that, by repeating such a branch-and-pruning procedure, it can achieve the optimal solution within finite iterations. A computationally efficient solver based on BPGrad has been proposed to train the deep neural networks. Empirical results demonstrate that BPGrad solver works well in practice and compares favorably to other stochastic optimization methods in the tasks of object recognition, detection, and segmentation. The code is available at \url{https://github.com/RyanCV/BPGrad}.