随机梯度下降,按照数据生成分布抽取m个样本,通过计算他们梯度的平均值来更新梯度。

VIP内容

题目: On the Generalization Benefit of Noise in Stochastic Gradient Descent

摘要:

长期以来一直有人认为,在深度神经网络中,小批量随机梯度下降比大批量梯度下降具有更好的泛化能力。但是,最近的论文对此主张提出了质疑,认为这种影响仅是批处理量较大时超优化超参数调整或计算预算不足的结果。在本文中,我们对一系列流行的模型进行了精心设计的实验并进行了严格的超参数扫描,这证明了小批量或中等批量都可以大大胜过测试集上的超大批量。即使两个模型都经过相同数量的迭代训练并且大批量实现较小的训练损失时,也会发生这种情况。我们的结果证实,随机梯度中的噪声可以增强泛化能力。我们研究最佳学习率时间表如何随着epoch budget的增长而变化,并基于SGD动力学的随机微分方程视角为我们的观察提供理论解释。

成为VIP会员查看完整内容
0
14

最新内容

Communication between workers and the master node to collect local stochastic gradients is a key bottleneck in a large-scale federated learning system. Various recent works have proposed to compress the local stochastic gradients to mitigate the communication overhead. However, robustness to malicious attacks is rarely considered in such a setting. In this work, we investigate the problem of Byzantine-robust federated learning with compression, where the attacks from Byzantine workers can be arbitrarily malicious. We point out that a vanilla combination of compressed stochastic gradient descent (SGD) and geometric median-based robust aggregation suffers from both stochastic and compression noise in the presence of Byzantine attacks. In light of this observation, we propose to jointly reduce the stochastic and compression noise so as to improve the Byzantine-robustness. For the stochastic noise, we adopt the stochastic average gradient algorithm (SAGA) to gradually eliminate the inner variations of regular workers. For the compression noise, we apply the gradient difference compression and achieve compression for free. We theoretically prove that the proposed algorithm reaches a neighborhood of the optimal solution at a linear convergence rate, and the asymptotic learning error is in the same order as that of the state-of-the-art uncompressed method. Finally, numerical experiments demonstrate effectiveness of the proposed method.

0
0
下载
预览

最新论文

Communication between workers and the master node to collect local stochastic gradients is a key bottleneck in a large-scale federated learning system. Various recent works have proposed to compress the local stochastic gradients to mitigate the communication overhead. However, robustness to malicious attacks is rarely considered in such a setting. In this work, we investigate the problem of Byzantine-robust federated learning with compression, where the attacks from Byzantine workers can be arbitrarily malicious. We point out that a vanilla combination of compressed stochastic gradient descent (SGD) and geometric median-based robust aggregation suffers from both stochastic and compression noise in the presence of Byzantine attacks. In light of this observation, we propose to jointly reduce the stochastic and compression noise so as to improve the Byzantine-robustness. For the stochastic noise, we adopt the stochastic average gradient algorithm (SAGA) to gradually eliminate the inner variations of regular workers. For the compression noise, we apply the gradient difference compression and achieve compression for free. We theoretically prove that the proposed algorithm reaches a neighborhood of the optimal solution at a linear convergence rate, and the asymptotic learning error is in the same order as that of the state-of-the-art uncompressed method. Finally, numerical experiments demonstrate effectiveness of the proposed method.

0
0
下载
预览
Top