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浙江大学学报(工学版)  2026, Vol. 60 Issue (10): 2247-2258    DOI: 10.3785/j.issn.1008-973X.2026.10.017
计算机技术与控制工程     
随机方差缩减的递归动量策略梯度方法
辛垚辉(),李永强*(),冯宇,胡磊
浙江工业大学 信息工程学院,浙江 杭州 310000
Stochastic variance-reduced recursive momentum policy gradient method
Yaohui XIN(),Yongqiang LI*(),Yu FENG,Lei HU
School of Information Engineering, Zhejiang University of Technology, Hangzhou 310000, China
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摘要:

强化学习中的策略梯度方法在梯度估计过程中通常存在方差过大的问题, 导致收敛性较差,为此提出随机方差缩减的递归动量策略梯度方法(SVRRM-PG). 通过结合重要性采样技术与参考点切换机制, 不需要使用重采样即可实现大批量梯度估计, 有效减小方差并提升训练稳定性,拥有可证明的、当前最优的样本复杂度. 为提升算法通用性, 将SVRRM-PG与近端策略优化(PPO)算法进行深度结合, 提出SVR-PPO算法, 以验证SVRRM-PG估计器在增强主流强化学习算法性能方面的有效性. 在多个经典离散与连续控制任务中进行性能对比,结果表明,SVRRM-PG估计器不仅能够有效提升收敛速度和稳定性,而且在多项基准测试中表现出优于现有方法的综合性能,验证了其在复杂强化学习场景下的有效性.

关键词: 强化学习策略梯度随机方差重要性采样样本复杂度    
Abstract:

In reinforcement learning, policy gradient methods are often challenged by excessive variance in gradient estimation, which leads to poor convergence. A stochastic variance-reduced recursive momentum policy gradient method (SVRRM-PG) was proposed. This method combines importance sampling technique with a reference-point switching mechanism to achieve large-batch gradient estimation without resampling, effectively reducing variance and improving training stability, while exhibiting provably advanced sample complexity currently. To improve the general applicability, the SVRRM-PG framework was integrated with the proximal policy optimization (PPO) algorithm, which led to the proposed SVR-PPO method for verifying the efficacy of SVRRM-PG estimator in enhancing the performance of the established reinforcement learning algorithms. A lot of benchmark discrete and continuous control tasks were conducted to compare the performance. The results demonstrate that the SVRRM-PG estimator not only accelerates the convergence significantly and improves the training stability, while achieves superior overall performance in multiple benchmark evaluations, confirming its effectiveness and robustness in complex reinforcement learning environments.

Key words: reinforcement learning    policy gradient    stochastic variance    importance sampling    sample complexity
收稿日期: 2025-06-06 出版日期: 2026-07-28
CLC:  TP 18  
基金资助: 国家自然科学基金资助项目(U2341216).
通讯作者: 李永强     E-mail: a13353745863@163.com;yqli@zjut.edu.cn
作者简介: 辛垚辉(2000—),男,硕士生,从事多智能体强化学习与博弈论研究. orcid.org/0009-0001-6228-0656. E-mail:a13353745863@163.com
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引用本文:

辛垚辉,李永强,冯宇,胡磊. 随机方差缩减的递归动量策略梯度方法[J]. 浙江大学学报(工学版), 2026, 60(10): 2247-2258.

Yaohui XIN,Yongqiang LI,Yu FENG,Lei HU. Stochastic variance-reduced recursive momentum policy gradient method. Journal of ZheJiang University (Engineering Science), 2026, 60(10): 2247-2258.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2026.10.017        https://www.zjujournals.com/eng/CN/Y2026/V60/I10/2247

方法VR技术样本复杂度小样本复杂度
GPOMDP[7]$ \mathcal{O}({\epsilon }^{-4}) $
SVRPG[18]SVRG[13]$ \mathcal{O}({\epsilon }^{-10/3}) $$ \mathcal{O}({\epsilon }^{-4/3}) $
STORM-PG[20]SARAH[14]$ \mathcal{O}({\epsilon }^{-3}) $$ \mathcal{O}(1) $
PAGE-PG[21]PAGE[17]$ \mathcal{O}({\epsilon }^{-3}) $$ \mathcal{O}(1) $
SVRRM-PGSVRRM[24]$ \mathcal{O}({\epsilon }^{-3}) $$ \mathcal{O}(1) $
表 1  部分算法对寻找$ \epsilon $-稳定解的复杂度实例
任务描述动作空间状态空间最大步长
Cartpole平衡车2维离散4维500
Acrobot两关节连杆3维离散6维500
Hopper跳跃机器人3维连续11维1000
Walker行走机器人6维连续17维1000
表 2  实验任务场景关键参数
算法$ \gamma $$ \eta $$ \alpha $$ p_{t} $$ {p}_{0} $$ S_{1} $$ B $$ Q $
GPOMDP0.990.01
STORM-PG0.990.010.9205
PAGE-PG0.990.010.3205
SHARP0.990.010.9205
SVRRM-PG0.990.010.90.3205100
表 3  基准实验参数设置
图 1  5种算法在离散任务上的奖励曲线
图 2  5种算法在连续任务上的奖励曲线
算法AcrobotCartpoleHopperWalker
0~30%30%~100%0~30%30%~100%0~30%30%~100%0~30%30%~100%
GPOMDP6383.36762.243726.2583.8073250.8637910.807108.043110.71
STORM-PG5577.74296.932025.4467.3580832.2520085.554739.302500.16
PAGE-PG5178.15247.353472.70104.6057135.1325513.845098.692666.30
SHARP4634.38308.802542.07152.4145235.574477.664100.442607.13
SVRRM-PG3531.65163.941817.9953.9038120.922744.553205.001836.84
表 4  5种实验算法在不同阶段的方差
$ Q $-$ B $R
0$ \sim $30003000$ \sim $10000
20-5155.87190.79
50-5155.87191.28
50-10137.84191.63
100-5157.91193.57
100-10139.50192.69
100-20108.91193.71
150-5157.01189.44
150-10140.52191.80
150-20110.50191.77
表 5  不同批量下的平均回报
图 3  不同批量下SVRRM-PG在Cartpole上的平均回报
算法t
AcrobotCartpoleHopperWalker
GPOMDP3′06″13′10″33′36″36′05″
STORM-PG2′16″14′22″38′50″38′10″
PAGE-PG2′21″13′12″35′18″35′10″
SHARP2′19″14′00″38′16″38′52″
SVRRM-PG2′26″15′40″41′24″42′37″
表 6  5种算法在不同任务上的运行时间
图 4  SVR-PPO与PPO在Walker任务上的平均回报
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