高级搜索

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于历史梯度平均方差缩减的协同参数更新方法

谢涛 张春炯 徐永健

谢涛, 张春炯, 徐永健. 基于历史梯度平均方差缩减的协同参数更新方法[J]. 电子与信息学报, 2021, 43(4): 956-964. doi: 10.11999/JEIT200061
引用本文: 谢涛, 张春炯, 徐永健. 基于历史梯度平均方差缩减的协同参数更新方法[J]. 电子与信息学报, 2021, 43(4): 956-964. doi: 10.11999/JEIT200061
Tao XIE, Chunjiong ZHANG, Yongjian XU. Collaborative Parameter Update Based on Average Variance Reduction of Historical Gradients[J]. Journal of Electronics & Information Technology, 2021, 43(4): 956-964. doi: 10.11999/JEIT200061
Citation: Tao XIE, Chunjiong ZHANG, Yongjian XU. Collaborative Parameter Update Based on Average Variance Reduction of Historical Gradients[J]. Journal of Electronics & Information Technology, 2021, 43(4): 956-964. doi: 10.11999/JEIT200061

基于历史梯度平均方差缩减的协同参数更新方法

doi: 10.11999/JEIT200061
基金项目: 国家自然科学基金(61807027)
详细信息
    作者简介:

    谢涛:男,1983年生,博士,副教授,研究方向为数据挖掘、自适应推荐系统、机器学习

    张春炯:男,1990年生,博士生,研究方向为机器学习、无线传感网络、分布式鲁棒优化

    徐永健:男,1997年生,硕士生,研究方向为图像检索、分布式系统

    通讯作者:

    谢涛 xietao@swu.edu.cn

  • 中图分类号: TP391

Collaborative Parameter Update Based on Average Variance Reduction of Historical Gradients

Funds: The National Natural Science Foundation of China (61807027)
  • 摘要: 随机梯度下降算法(SGD)随机使用一个样本估计梯度,造成较大的方差,使机器学习模型收敛减慢且训练不稳定。该文提出一种基于方差缩减的分布式SGD,命名为DisSAGD。该方法采用历史梯度平均方差缩减来更新机器学习模型中的参数,不需要完全梯度计算或额外存储,而是通过使用异步通信协议来共享跨节点的参数。为了解决全局参数分发存在的“更新滞后”问题,该文采用具有加速因子的学习速率和自适应采样策略:一方面当参数偏离最优值时,增大加速因子,加快收敛速度;另一方面,当一个工作节点比其他工作节点快时,为下一次迭代采样更多样本,使工作节点有更多时间来计算局部梯度。实验表明:DisSAGD显著减少了循环迭代的等待时间,加速了算法的收敛,其收敛速度比对照方法更快,在分布式集群中可以获得近似线性的加速。
  • 图  1  分布式机器学习拓扑

    图  2  不同加速因子在独立节点运行损失函数值的变化

    图  3  不同算法之间收敛性能比较

    图  4  DisSAGD算法中不同工作节点数量的加速效果

    图  5  自适应采样对收敛和等待时间影响

    图  6  不同延迟时间对平均等待时间和平均计算时间的影响

    图  7  平均等待时间和平均计算时间的平衡

    表  1  基于历史梯度平均方差缩减算法

     输入:learning rate $\lambda $.
     输出:$\omega $ and $g$ for next epoch.
     (1) Initialize $\omega $ using plain SGD for 1 epoch;
     (2) while not converged do
     (3) $\overline \omega \leftarrow 0$;
     (4) $\overline g \leftarrow 0$;
     (5) for $t$= 0, 1, ···, T do
     (6)  Randomly sample ${i_t} = \{ 1,2,··· ,m\}$ without replacement;
     (7)  $\overline \omega \leftarrow \frac{1}{m}\displaystyle\sum\limits_{i = 1}^m { {\omega _i} }$;
     (8)  $\overline g \leftarrow \frac{1}{m}\displaystyle\sum\limits_{i = 1}^m {\nabla {f_i}({\omega _i})}$;
     (9)  Update $g$ and $\omega $ using equation(1) and equation(3),
         respectively;
     (10) end
     (11) end
    下载: 导出CSV

    表  2  DisSAGD算法的伪代码

     输入:${D_1},{D_2}, ··· ,{D_p}$.
     输出:${\omega _1},{\omega _2}, ··· ,{\omega _p}$.
     (1) Initialize ${\omega _p}$;
     (2) for s = 1, 2, ···, N do
     (3) for each node $k \in \{ 1,2, ··· ,p\} $do
     (4) Call subroutine avr_hg($\lambda $);
     (5) end
     (6) Return all ${\omega _{k,t}}$ and ${f_{k,t}}(\omega )$ from node k to server;
     (7) Compute ${\omega ^{s - 1} } = \dfrac{1}{k}\displaystyle\sum\limits_{i = 1}^k { {\omega _i} }$ and $f(\omega )$ using equation(4)
        on the server side;
     (8)  ${\omega ^s} = {\omega ^{s - 1} } - {\lambda _{s - 1} }\dfrac{1}{k}\displaystyle\sum\limits_{i = 1}^k {\nabla {f_i}(\omega )}$;
     (9) end
     (10) ${\omega _p} \leftarrow {\omega ^s}$;
    下载: 导出CSV

    表  3  模型的F1

    SVHNCifar100KDDcup99
    PetuumSGD0.95470.66840.9335
    SSGD0.96750.66910.9471
    DisSVRG0.96880.67760.9441
    ASD-SVRG0.98310.68340.9512
    DisSAGD0.98270.69020.9508
    DisSAGD-tricks0.99820.70860.9588
    下载: 导出CSV
  • 周辉林, 欧阳韬, 刘健. 基于随机平均梯度下降和对比源反演的非线性逆散射算法研究[J]. 电子与信息学报, 2020, 42(8): 2053–2058. doi: 10.11999/JEIT190566

    ZHOU Huilin, OUYANG Tao, and LIU Jian. Stochastic average gradient descent contrast source inversion based nonlinear inverse scattering method for complex objects reconstruction[J]. Journal of Electronics &Information Technology, 2020, 42(8): 2053–2058. doi: 10.11999/JEIT190566
    XING E P, HO Q, DAI Wei, et al. Petuum: A new platform for distributed machine learning on big data[J]. IEEE Transactions on Big Data, 2015, 1(2): 49–67. doi: 10.1109/TBDATA.2015.2472014
    HO Qirong, CIPAR J, CUI Henggang, et al. More effective distributed ml via a stale synchronous parallel parameter server[C]. Advances in Neural Information Processing Systems, Stateline, USA, 2013: 1223–1231.
    SHI Hang, ZHAO Yue, ZHANG Bofeng, et al. A free stale synchronous parallel strategy for distributed machine learning[C]. The 2019 International Conference on Big Data Engineering, Hong Kong, China, 2019: 23–29. doi: 10.1145/3341620.3341625.
    ZHAO Xing, AN Aijun, LIU Junfeng, et al. Dynamic stale synchronous parallel distributed training for deep learning[C]. 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS), Dallas, USA, 2019: 1507–1517. doi: 10.1109/ICDCS.2019.00150.
    DEAN J, CORRADO G S, MONGA R, et al. Large scale distributed deep networks[C]. The 25th International Conference on Neural Information Processing Systems, Red Hook, USA, 2012: 1223–1231.
    赵小强, 宋昭漾. 多级跳线连接的深度残差网络超分辨率重建[J]. 电子与信息学报, 2019, 41(10): 2501–2508. doi: 10.11999/JEIT190036

    ZHAO Xiaoqiang and SONG Zhaoyang. Super-resolution reconstruction of deep residual network with multi-level skip connections[J]. Journal of Electronics &Information Technology, 2019, 41(10): 2501–2508. doi: 10.11999/JEIT190036
    LI Mu, ANDERSEN D G, PARK J W, et al. Scaling distributed machine learning with the parameter server[C]. The 2014 International Conference on Big Data Science and Computing, Beijing, China, 2014: 583–598. https://doi.org/10.1145/2640087.2644155.
    ZHANG Ruiliang, ZHENG Shuai, and KWOK J T. Asynchronous distributed semi-stochastic gradient optimization[C]. The Thirtieth AAAI Conference on Artificial Intelligence, Phoenix, USA, 2016: 2323–2329.
    XIE Pengtao, KIM J K, ZHOU Yi, et al. Distributed machine learning via sufficient factor broadcasting[J]. arXiv: 1511. 08486, 2015.
    LI Mu, ZHANG Tong, CHEN Yuqiang, et al. Efficient mini-batch training for stochastic optimization[C]. The 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, USA, 2014: 661–670. doi: 10.1145/2623330.2623612.
    WU Jiaxiang, HUANG Weidong, HUANG Junzhou, et al. Error compensated quantized SGD and its applications to large-scale distributed optimization[C]. The 35th International Conference on Machine Learning, Stockholm, The Kingdom of Sweden, 2018.
    LE ROUX N, SCHMIDT M, and BACH F. A stochastic gradient method with an exponential convergence rate for finite training sets[C]. The 26th Annual Conference on Neural Information Processing Systems, Lake Tahoe, USA, 2012: 2663–2671.
    DEFAZIO A, BACH F, and LACOSTE-JULIEN S. SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives[C]. The 27th International Conference on Neural Information Processing Systems, Cambridge, USA, 2014: 1646–1654.
    BAN Zhihua, LIU Jianguo, and CAO Li. Superpixel segmentation using Gaussian mixture model[J]. IEEE Transactions on Image Processing, 2018, 27(8): 4105–4117. doi: 10.1109/TIP.2018.2836306
    WANG Pengfei, LIU Risheng, ZHENG Nenggan, et al. Asynchronous proximal stochastic gradient algorithm for composition optimization problems[J]. Proceedings of the AAAI Conference on Artificial Intelligence, 2019, 33(1): 1633–1640. doi: 10.1609/aaai.v33i01.33011633
    FERRANTI L, PU Ye, JONES C N, et al. SVR-AMA: An asynchronous alternating minimization algorithm with variance reduction for model predictive control applications[J]. IEEE Transactions on Automatic Control, 2019, 64(5): 1800–1815. doi: 10.1109/TAC.2018.2849566
    邵言剑, 陶卿, 姜纪远, 等. 一种求解强凸优化问题的最优随机算法[J]. 软件学报, 2014, 25(9): 2160–2171. doi: 10.13328/j.cnki.jos.004633

    SHAO Yanjian, TAO Qing, JIANG Jiyuan, et al. Stochastic algorithm with optimal convergence rate for strongly convex optimization problems[J]. Journal of Software, 2014, 25(9): 2160–2171. doi: 10.13328/j.cnki.jos.004633
    赵海涛, 程慧玲, 丁仪, 等. 基于深度学习的车联边缘网络交通事故风险预测算法研究[J]. 电子与信息学报, 2020, 42(1): 50–57. doi: 10.11999/JEIT190595

    ZHAO Haitao, CHENG Huiling, DING Yi, et al. Research on traffic accident risk prediction algorithm of edge internet of vehicles based on deep learning[J]. Journal of Electronics &Information Technology, 2020, 42(1): 50–57. doi: 10.11999/JEIT190595
    RAMAZANLI I, NGUYEN H, PHAM H, et al. Adaptive sampling distributed stochastic variance reduced gradient for heterogeneous distributed datasets[J]. arXiv: 2002. 08528, 2020.
    SUSSMAN D M. CellGPU: Massively parallel simulations of dynamic vertex models[J]. Computer Physics Communications, 2017, 219: 400–406. doi: 10.1016/j.cpc.2017.06.001
  • 加载中
图(7) / 表(3)
计量
  • 文章访问数:  2359
  • HTML全文浏览量:  918
  • PDF下载量:  87
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-01-16
  • 修回日期:  2020-06-20
  • 网络出版日期:  2020-07-23
  • 刊出日期:  2021-04-20

目录

    /

    返回文章
    返回