异策略深度强化学习中的经验回放研究综述

胡子剑; 高晓光; 万开方; 张乐天; 汪强龙; NERETIN Evgeny

doi:10.16383/j.aas.c220648

异策略深度强化学习中的经验回放研究综述

doi: 10.16383/j.aas.c220648

1.
西北工业大学电子信息学院西安 710129 中国
2.
西安电子科技大学外国语学院西安 710126 中国
3.
莫斯科航空学院机器人与智能系统学院莫斯科 125993 俄罗斯

基金项目: 国家自然科学基金(62003267, 61573285), 中央高校基本科研业务费专项资金(G2022KY0602), 电磁空间作战与应用重点实验室(2022ZX0090), 西安市科技计划项目 —— 关键核心技术攻关工程项目计划(21RGZN0016), 陕西省重点研发计划项目(2023-GHZD-33)资助

详细信息

作者简介:
胡子剑：西北工业大学电子信息学院博士研究生. 2018 年获得西北工业大学探测制导与控制技术学士学位. 主要研究方向为强化学习理论与应用. E-mail: huzijian@mail.nwpu.edu.cn

高晓光：西北工业大学电子信息学院教授. 1989 年获得西北工业大学系统工程博士学位. 主要研究方向为机器学习理论, 贝叶斯网络理论和多智能体控制应用. E-mail: cxg2012@nwpu.edu.cn

万开方：西北工业大学电子信息学院副研究员. 2016 年获得西北工业大学系统工程博士学位. 主要研究方向为多智能体理论, 近似动态规划和强化学习. 本文通信作者. E-mail: wankaifang@nwpu.edu.cn

张乐天：西安电子科技大学外国语学院硕士研究生. 主要研究方向为科技翻译, 翻译理论和机器翻译. E-mail: 22091213382@stu.xidian.edu.cn

汪强龙：西北工业大学电子信息学院博士研究生. 主要研究方向为深度学习, 强化学习. E-mail: wql1995@mail.nwpu.edu.cn

NERETIN Evgeny：莫斯科航空学院教授. 2011年获得莫斯科航空学院技术科学博士学位. 主要研究方向为航空电子, 智能决策. E-mail: evgeny.neretin@gmail.com

计量
- 文章访问数: 3875
- HTML全文浏览量: 937
- PDF下载量: 695
- 被引次数: 0
出版历程
- 收稿日期: 2022-08-18
- 录用日期: 2023-01-21
- 网络出版日期: 2023-03-28
- 刊出日期: 2023-11-22

Research on Experience Replay of Off-policy Deep Reinforcement Learning: A Review

1.
School of Electronics and Information, Northwestern Polytechnical University, Xi＇an 710129, China
2.
School of Foreign Languages, Xidian University, Xi＇an 710126, China
3.
School of Robotic and Intelligent Systems, Moscow Aviation Institute (National Research University), Moscow 125993, Russia

Funds: Supported by National Natural Science Foundation of China (62003267, 61573285), the Fundamental Research Funds for the Central Universities (G2022KY0602), the Technology on Electromagnetic Space Operations and Applications Laboratory (2022ZX0090), the Key Core Technology Research Plan of Xi＇an (21RGZN0016), and the Key Research and Development Program of Shaanxi Province (2023-GHZD-33)

More Information

Author Bio:
HU Zi-Jian　Ph.D. candidate at the School of Electronics and Information, Northwestern Polytechnical University. He received his bachelor degree in detection guidance and control technology from Northwestern Polytechnical University in 2018. His research interest covers reinforcement learning theory and applications

GAO Xiao-Guang　Professor at the School of Electronics and Information, Northwestern Polytechnical University. She received her Ph.D. degree in system engineering from Northwestern Polytechnical University in 1989. Her research interest covers machine learning theory, Bayesian network theory, and multi-agent control application

WAN Kai-Fang　Associate researcher at the School of Electronics and Information, Northwestern Polytechnical University. He received his Ph.D. degree in system engineering from Northwestern Polytechnical University in 2016. His research interest covers multi-agent theory, approximate dynamic programming, and reinforcement learning. Corresponding author of this paper

ZHANG Le-Tian　Master student at the School of Foreign Languages, Xidian University. Her research interest covers scientific translation, translation theory, and machine translation

WANG Qiang-Long　Ph.D. candidate at the School of Electronics and Information, Northwestern Polytechnical University. His research interest covers deep learning and reinforcement learning

NERETIN Evgeny　Professor of Moscow Aviation Institute. He received his Ph.D. degree in technical sciences from Moscow Aviation Institute in 2011. His research interest covers avionics and intelligent decision-making

摘要

摘要: 作为一种不需要事先获得训练数据的机器学习方法, 强化学习(Reinforcement learning, RL)在智能体与环境的不断交互过程中寻找最优策略, 是解决序贯决策问题的一种重要方法. 通过与深度学习(Deep learning, DL)结合, 深度强化学习(Deep reinforcement learning, DRL)同时具备了强大的感知和决策能力, 被广泛应用于多个领域来解决复杂的决策问题. 异策略强化学习通过将交互经验进行存储和回放, 将探索和利用分离开来, 更易寻找到全局最优解. 如何对经验进行合理高效的利用是提升异策略强化学习方法效率的关键. 首先对强化学习的基本理论进行介绍; 随后对同策略和异策略强化学习算法进行简要介绍; 接着介绍经验回放(Experience replay, ER)问题的两种主流解决方案, 包括经验利用和经验增广; 最后对相关的研究工作进行总结和展望.
- 深度强化学习 /
- 异策略 /
- 经验回放 /
- 人工智能
Abstract: As a machine learning method that does not need to obtain training data in advance, reinforcement learning (RL) is an important method to solve the sequential decision-making problem by finding the optimal strategy in the continuous interaction between the agent and the environment. Through the combination of deep learning (DL), deep reinforcement learning (DRL) has both powerful perception and decision-making capabilities, and is widely used in many fields to solve complex decision-making problems. Off-policy reinforcement learning separates exploration and utilization by storing and replaying interactive experience, making it easier to find the global optimal solution. How to make reasonable and efficient use of experience is the key to improve the efficiency of off-policy reinforcement learning methods. First, this paper introduces the basic theory of reinforcement learning. Then, the on-policy and off-policy reinforcement learning algorithms are briefly introduced. Next, two mainstream solutions of experience replay (ER) problem are introduced, including experience utilization and experience expansion. Finally, the relevant research work is summarized and prospected.
- Deep reinforcement learning (DRL) /
- off-policy /
- experience replay (ER) /
- artificial intelligence

HTML全文

图 1 强化学习过程

Fig. 1 The process of reinforcement learning

下载: 全尺寸图片幻灯片

图 2 强化学习算法分类

Fig. 2 The classification of reinforcement learning algorithms

下载: 全尺寸图片幻灯片

图 3 DQN算法框架

Fig. 3 The framework of DQN algorithm

下载: 全尺寸图片幻灯片

图 4 DDPG算法框架

Fig. 4 The framework of DDPG algorithm

下载: 全尺寸图片幻灯片

图 5 异策略RL的经验回放流程

Fig. 5 The experience replay process of off-policy RL

下载: 全尺寸图片幻灯片

图 6 经验回放分类

Fig. 6 The classification of experience replay

下载: 全尺寸图片幻灯片

图 7 QER的算法框架

Fig. 7 The framework of QER algorithm

下载: 全尺寸图片幻灯片

图 8 “sum-tree” 采样流程

Fig. 8 The sampling process of “sum-tree”

下载: 全尺寸图片幻灯片

图 9 “double sum-tree” 数据结构

Fig. 9 The data structure of “double sum-tree”

下载: 全尺寸图片幻灯片

图 10 模型经验增广算法的框架图

Fig. 10 The framework of model experience augmentation algorithms

下载: 全尺寸图片幻灯片

表 1 同策略与异策略算法的优势对比

Table 1 Comparison of advantages of on-policy and off-policy algorithms

算法优势	同策略RL	异策略RL
收敛速度更快	√
训练过程更稳定	√
超参数对算法影响更小	√
可以平衡探索和利用的问题		√
更易收敛到最优解		√
经验来源更广		√
经验的利用率更高		√
算法的适用范围更广		√

下载: 导出CSV

表 2 经验优先回放算法对比

Table 2 Comparison of prioritized experience replay algorithms

算法	优先回放指标	采样轮次
PER^[43], PSER^[44], PPER^[45]	TD error	单轮
HVPER^[46]	Q值, TD error	单轮
TASM^[47]	序列累计奖励, TD error	多轮
AER^[48]	相似性	多轮
REL^[49]	TD error, 相似性	多轮
KLPER^[50]	批量经验策略的相似性	单轮
DCRL^[51]	经验难度, 采样次数	单轮
ACER^[54]	经验难度	单轮

下载: 导出CSV

表 3 经验分类回放算法对比

Table 3 Comparison of classification experience replay algorithms

算法	分类标准	经验池形式	采样策略
CER^[59]	是否为当前经验	单经验池 + 临时存储	随机采样 + 当前经验
ACER^[54]	是否为最新经验	多经验池	优先采样 + 最新经验
ReFER^[60]	经验策略与当前策略的差异	单经验池	随机采样 + 经验过滤
RC^[61]	奖励	多经验池	静态采样
TDC^[61]	TD error	多经验池	静态采样
EPS^[49]	基于场景的评价指标	多经验池 + 单经验池	静态采样
CADP^[62]	TD error	多经验池	动态采样
DDN-SDRL^[63]	状态的危险程度	多经验池	静态采样

下载: 导出CSV

表 4 经验存储结构算法的优化途径

Table 4 Optimization approaches of experience storage structure algorithms

算法	数据结构	更新逻辑	硬件架构
PER^[43]	√
ACER^[54]	√	√
LSER^[66]		√
DER^[67]		√
AMPER^[68]	√		√

下载: 导出CSV

表 5 专家示范经验算法对比

Table 5 Comparison of expert demonstration experience algorithms

算法	专家经验来源	专家经验作用方式	经验池形式	采样策略	应用场景
DQfD^[71]	人类示范	预训练	单经验池	优先采样	视频游戏
DDPGfD^[72]	人类示范	实际训练	单经验池	优先采样	机械臂控制
LfOD^[73]	仿真平台	专家网络 + 实际训练	多经验池	动态采样 + 优先采样	自动路口管理
IEP^[74]	人类示范	专家网络 + 实际训练	单经验池	随机采样	自动驾驶
MEP^[75]	模拟退火算法	实际训练	多经验池	动态采样	无人机运动控制
ME^[76]	人工势场法	实际训练	多经验池	动态采样	多无人车运动规划
VD4^[78]	人类示范	预训练 + 实际训练	多经验池	优先采样	自主水下航行器控制

下载: 导出CSV

参考文献(90)

[1]	高阳, 陈世福, 陆鑫. 强化学习研究综述. 自动化学报, 2004, 30(1): 86-100 Gao Yang, Chen Shi-Fu, Lu Xin. Research on reinforcement learning technology: A review. Acta Automatica Sinica, 2004, 30(1): 86-100
[2]	Sutton R S, Barto A G. Reinforcement Learning: An Introduction. Cambridge: MIT Press, 1998.
[3]	李晨溪, 曹雷, 张永亮, 陈希亮, 周宇欢, 段理文. 基于知识的深度强化学习研究综述. 系统工程与电子技术, 2017, 39(11): 2603-2613 doi: 10.3969/j.issn.1001-506X.2017.11.30 Li Chen-Xi, Cao Lei, Zhang Yong-Liang, Chen Xi-Liang, Zhou Yu-Huan, Duan Li-Wen. Knowledge-based deep reinforcement learning: A review. Systems Engineering and Electronics, 39(11): 2603-2613 doi: 10.3969/j.issn.1001-506X.2017.11.30
[4]	Bellman R. Dynamic Programming. Princeton: Princeton University Press, 1957.
[5]	Mnih V, Kavukcuoglu K, Silver D, Rusu A A, Veness J, Bellemare M G, et al. Human-level control through deep reinforcement learning. Nature, 2015, 518(7540): 529-533 doi: 10.1038/nature14236
[6]	刘全, 翟建伟, 章宗长, 钟珊, 周倩, 章鹏, 等. 深度强化学习综述. 计算机学报, 2018, 48(1): 1-27 doi: 10.11897/SP.J.1016.2019.00001 Liu Quan, Zhai Jian-Wei, Zhang Zong-Chang, Zhong Shan, Zhou Qian, Zhang Peng, et al. A survey on deep reinforcement learning. Chinese Journal of Computers, 2018, 48(1): 1-27 doi: 10.11897/SP.J.1016.2019.00001
[7]	Mnih V, Kavukcuoglu K, Silver D, Graves A, Antonoglou I, Wierstra D, et al. Playing Atari with deep reinforcement learning. arXiv preprint arXiv: 1312.5602, 2013.
[8]	Cheng Y H, Chen L, Chen C L P, Wang X S. Off-policy deep reinforcement learning based on Steffensen value iteration. IEEE Transactions on Cognitive and Developmental Systems, 2021, 13(4): 1023-1032 doi: 10.1109/TCDS.2020.3034452
[9]	Silver D, Huang A, Maddison C J, Guez A, Sifre L, Driessche G V D, et al. Mastering the game of Go with deep neural networks and tree search. Nature, 2016, 529(7587): 484-489 doi: 10.1038/nature16961
[10]	Chen P Z, Lu W Q. Deep reinforcement learning based moving object grasping. Information Sciences, 2021, 565: 62-76. doi: 10.1016/j.ins.2021.01.077
[11]	Jin Z H, Wu J H, Liu A D, Zhang W A, Yu L. Policy-based deep reinforcement learning for visual servoing control of mobile robots with visibility constraints. IEEE Transactions on Industrial Electronics, 2022, 69(2): 1898-1908 doi: 10.1109/TIE.2021.3057005
[12]	Li X J, Liu H S, Dong M H. A general framework of motion planning for redundant robot manipulator based on deep reinforcement learning. IEEE Transactions on Industrial Informatics, 2022, 18(8): 5253-5263 doi: 10.1109/TII.2021.3125447
[13]	Chen S Y, Wang M L, Song W J, Yang Y, Li Y J, Fu M Y. Stabilization approaches for reinforcement learning-based end-to-end autonomous driving. IEEE Transactions on Vehicular Technology, 2020, 69(5): 4740-4750 doi: 10.1109/TVT.2020.2979493
[14]	Qi Q, Zhang L X, Wang J Y, Sun H F, Zhuang Z R, Liao J X, et al. Scalable parallel task scheduling for autonomous driving using multi-task deep reinforcement learning. IEEE Transactions on Vehicular Technology, 2020, 69(11): 13861-13874 doi: 10.1109/TVT.2020.3029864
[15]	Kiran B R, Sobh I, Talpaert V, Mannion P, Sallab A A A, Yogamani S, et al. Deep reinforcement learning for autonomous driving: A survey. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(6): 4909-4926 doi: 10.1109/TITS.2021.3054625
[16]	Taghian M, Asadi A, Safabakhsh R. Learning financial asset-specific trading rules via deep reinforcement learning. Expert Systems with Applications, 2022, 195: Article No. 116523 doi: 10.1016/j.eswa.2022.116523
[17]	Tsantekidis A, Passalis N, Tefas A. Diversity-driven knowledge distillation for financial trading using Deep Reinforcement Learning. Neural Networks, 2021, 140: 193-202 doi: 10.1016/j.neunet.2021.02.026
[18]	Park H, Sim M K, Choi D G. An intelligent financial portfolio trading strategy using deep Q-learning. Expert Systems with Applications, 2020, 158: Article No. 113573 doi: 10.1016/j.eswa.2020.113573
[19]	Tan W S, Ryan M L. A single site investigation of DRLs for CT head examinations based on indication-based protocols in Ireland. Journal of Medical Imaging and Radiation Sciences, DOI: 10.1016/j.jmir.2022.03.114
[20]	Allahham M S, Abdellatif A A, Mohamed A, Erbad A, Yaacoub E, Guizani M. I-SEE: Intelligent, secure, and energy-efficient techniques for medical data transmission using deep reinforcement learning. IEEE Internet of Things Journal, 2021, 8(8): 6454-6468 doi: 10.1109/JIOT.2020.3027048
[21]	Lin L J. Self-improving reactive agents based on reinforcement learning, planning and teaching. Machine Learning, 1992, 8: 293-321
[22]	Bellman R. A Markovian decision process. Indiana University Mathematics Journal, 1957, 6(4): 679-684 doi: 10.1512/iumj.1957.6.56038
[23]	Rummery G A, Niranjan M. On-line Q-learning Using Connectionist Systems, Technical Report GUED/F-INFENG/TR 166, Engineering Department, Cambridge University, England, 1994.
[24]	Sutton R, Mcallester D A, Singh S, Mansour Y. Policy gradient methods for reinforcement learning with function approximation. In: Proceedings of the Advances in Neural Information Processing Systems (NIPS). Denver, Colorado, USA: MIT Press, 1999. 1057−1063
[25]	Williams R J. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning, 1992, 8: 229-256
[26]	Mnih V, Badia A P, Mirza M, Graves A, Harley T, Lillicrap P T, et al. Asynchronous methods for deep reinforcement learning. In: Proceedings of the 33rd International Conference on Machine Learning (ICML). New York, USA: ACM, 2016. 1928−1937
[27]	Babaeizadeh M, Frosio I, Tyree S, Clemons J, Kautz J. Reinforcement learning through asynchronous advantage actor-critic on a GPU. arXiv preprint arXiv: 1611.06256, 2017.
[28]	Schulman J, Levine S, Moritz P, Jordan M I, Abbeel P. Trust region policy optimization. arXiv preprint arXiv: 1502.05477, 2015.
[29]	Schulman J, Wolski F, Dhariwal P, Radford A, Klimov O. Proximal policy optimization algorithms. arXiv preprint arXiv: 1707.06347, 2017.
[30]	Watkins C J C H, Dayan P. Q-learning. Machine Learning, 1992, 8(3): 279-292
[31]	Hasselt H V, Guez A, Silver D. Deep reinforcement learning with double Q-learning. arXiv preprint arXiv: 1509.06461, 2015.
[32]	Wang Z Y, Tom S, Matteo H, Hado V H, Marc L, Nando D F. Dueling network architectures for deep reinforcement learning. In: Proceedings of the 33rd International Conference on Machine Learning (ICML). New York, USA: ACM, 2016. 1995−2003
[33]	Lillicrap T P, Hunt J J, Pritzel A, Heess N, Erez T, Tassa Y, et al. Continuous control with deep reinforcement learning. arXiv preprint arXiv: 1509.02971, 2015.
[34]	Fujimoto S, Hoof V H, Meger D. Addressing function approximation error in actor-critic methods. arXiv preprint arXiv: 1802.09477, 2018.
[35]	Haarnoja T, Zhou A, Abbeel P, Levine S. Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. arXiv preprint arXiv: 1801.01290, 2018.
[36]	Nair A, Srinivasan P, Blackwell S, Alcicek C, Fearon R, Maria A D, et al. Massively parallel methods for deep reinforcement learning. arXiv preprint arXiv: 1507.04296, 2015.
[37]	Hausknecht M, Stone P. Deep recurrent Q-learning for partially observable MDPs. arXiv preprint arXiv: 1507.06527, 2015.
[38]	Plappert M, Houthooft R, Dhariwal P, Sidor S, Chen R Y, Chen X, et al. Parameter space noise for exploration. arXiv preprint arXiv: 1706.01905, 2018.
[39]	Hessel M, Modayil J, Hasselt H V, Schaul T, Ostrovski G, Dabney W, et al. Rainbow: Combining improvements in deep reinforcement learning. arXiv preprint arXiv: 1710.02298, 2017.
[40]	刘建伟, 高峰, 罗雄麟. 基于值函数和策略梯度的深度强化学习综述. 计算机学报, 2019, 42(6): 1406-1438 doi: 10.11897/SP.J.1016.2019.01406 Liu Jian-Wei, Gao Feng, Luo Xiong-Lin. Survey of deep reinforcement learning based on value policy gradient. Chinese Journal of Computers, 2019, 42(6): 1406-1438 doi: 10.11897/SP.J.1016.2019.01406
[41]	Haarnoja T, Zhou A, Hartikainen K, Tucker G, Ha S, Tan J, et al. Soft actor-critic algorithms and applications. arXiv preprint arXiv: 1812.05905, 2018.
[42]	Jang E, Gu S X, Poole B. Categorical reparameterization with Gumbel-Softmax. arXiv preprint arXiv: 1611.01144, 2017.
[43]	Schaul T, Quan J, Antonoglou I, Silver D. Prioritized experience replay. arXiv preprint arXiv: 1511.05952, 2016.
[44]	Brittain M, Bertram J, Yang X X, Wei P. Prioritized sequence experience replay. arXiv preprint arXiv: 1905.12726, 2019.
[45]	Lee S, Lee J, Hasuo I. Predictive PER: Balancing priority and diversity towards stable deep reinforcement learning. arXiv preprint arXiv: 2011.13093, 2020.
[46]	Cao X, Wan H Y, Lin Y F, Han S. High-value prioritized experience replay for off-policy reinforcement learning. In: Proceedings of the IEEE 31st International Conference on Tools With Artificial Intelligence (ICTAI). Portland, OR, USA: IEEE, 2019. 1510−1514
[47]	赵英男, 刘鹏, 赵巍, 唐降龙. 深度 Q 学习的二次主动采样方法. 自动化学报, 2019, 45(10): 1870-1882 Zhao Ying-Nan, Liu Peng, Zhao Wei, Tang Jiang-Long. Twice sampling method in deep Q-network. Acta Automatica Sinica, 2019, 45(10): 1870-1882
[48]	Sun P Q, Zhou W G, Li H Q. Attentive experience replay. In: Proceedings of the 34th AAAI Conference on Artificial Intelligence. New York, USA: AAAI Press, 2020. 5900−5907
[49]	Hu Z J, Gao X G, Wan K F, Zhai Y W, Wang Q L. Relevant experience learning: A deep reinforcement learning method for UAV autonomous motion planning in complex unknown environments. Chinese Journal of Aeronautics, 2021, 34(12): 187-204 doi: 10.1016/j.cja.2020.12.027
[50]	Cicek D C, Duran E, Saglam B, Mutlu F B, Kozat S S. Off-policy correction for deep deterministic policy gradient algorithms via batch prioritized experience replay. In: Proceedings of the 33rd IEEE International Conference on Tools With Artificial Intelligence (ICTAI). Washington, DC, USA: IEEE, 2021. 1255−1262
[51]	Ren Z P, Dong D Y, Li H X, Chen C L. Self-paced prioritized curriculum learning with coverage penalty in deep reinforcement learning. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(6): 2216-2226 doi: 10.1109/TNNLS.2018.2790981
[52]	Bengio Y, Louradour J, Collobert R, Weston J. Curriculum learning. In: Proceedings of the 26th Annual International Conference on Machine Learning (ICML). Montreal, Quebec, Canada: ACM, 2009. 41−48
[53]	Wang X, Chen Y D, Zhu W W. A survey on curriculum learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022, 44(9): 4555-4576
[54]	Hu Z J, Gao X G, Wan K F, Wang Q L, Zhai Y W. Asynchronous curriculum experience replay: A deep reinforcement learning approach for UAV autonomous motion control in unknown dynamic environments. arXiv preprint arXiv: 2207.01251, 2022.
[55]	Kumar A, Gupta A, Levine S. DisCor: Corrective feedback in reinforcement learning via distribution correction. arXiv preprint arXiv: 2003.07305, 2020.
[56]	Lee K, Laskin M, Srinivas A, Abbeel P. SUNRISE: A simple unified framework for ensemble learning in deep reinforcement learning. arXiv preprint arXiv: 2007.04938, 2020.
[57]	Sinha S, Song J M, Garg A, Ermon S. Experience replay with likelihood-free importance weights. arXiv preprint arXiv: 2006.13169, 2020.
[58]	Liu X H, Xue Z H, Pang J C, Jiang S Y, Xu F, Yu Y. Regret minimization experience replay in off-policy reinforcement learning. arXiv preprint arXiv: 2105.07253, 2021.
[59]	Zhang S T, Sutton R S. A deeper look at experience replay. arXiv preprint arXiv: 1712.01275, 2018.
[60]	Novati G, Koumoutsakos P. Remember and forget for experience replay. arXiv preprint arXiv: 1807.05827, 2019.
[61]	时圣苗, 刘全. 采用分类经验回放的深度确定性策略梯度方法. 自动化学报, 2022, 48(7): 1816-1823 doi: 10.16383/j.aas.c190406 Shi Sheng-Miao, Liu Quan. Deep deterministic policy gradient with classified experience replay. Acta Automatica Sinica, 2022, 48(7): 1816-1823 doi: 10.16383/j.aas.c190406
[62]	刘晓宇, 许驰, 曾鹏, 于海斌. 面向异构工业任务高并发计算卸载的深度强化学习方法. 计算机学报, 2021, 44(12): 2367-2380 Liu Xiao-Yu, Xu Chi, Zeng Peng, Yu Hai-Bin. Deep reinforcement learning-based high concurrent computing offloading for heterogeneous industrial tasks. Chinese Journal of Computers, 2021, 44(12): 2367-2380
[63]	朱斐, 吴文, 伏玉琛, 刘全. 基于双深度网络的安全深度强化学习方法. 计算机学报, 2019, 42(8): 1812-1826 doi: 10.11897/SP.J.1016.2019.01812 Zhu Fei, Wu Wen, Fu Yu-Chen, Liu Quan. A dual deep network based secure deep reinforcement learning method. Chinese Journal of Computers, 2019, 42(8): 1812-1826 doi: 10.11897/SP.J.1016.2019.01812
[64]	Wei Q, Ma H L, Chen C L, Dong D Y. Deep reinforcement learning with quantum-inspired experience replay. IEEE Transactions on Cybernetics, 2022, 52(9): 9326-9338 doi: 10.1109/TCYB.2021.3053414
[65]	Li Y J, Aghvami A H, Dong D Y. Path planning for cellular-connected UAV: A DRL solution with quantum-inspired experience replay. IEEE Transactions on Wireless Communications, 2022, 21(10): 7897-7912 doi: 10.1109/TWC.2022.3162749
[66]	Chen X C, Yao L N, Wang X Z, McAuley J. Locality-sensitive experience replay for online recommendation. arXiv preprint arXiv: 2110.10850, 2021.
[67]	Bruin T D, Kober J, Tuyls K, Babuska R. Improved deep reinforcement learning for robotics through distribution-based experience retention. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Daejeon, South Korea: IEEE, 2016. 3947−3952
[68]	Li M Y, Kazemi A, Laguna A F, Hu X S. Associative memory based experience replay for deep reinforcement learning. arXiv preprint arXiv: 2207.07791, 2022.
[69]	Schaal S. Is imitation learning the route to humanoid robots? Trends in Cognitive Sciences, 1999, 3(6): 233-242 doi: 10.1016/S1364-6613(99)01327-3
[70]	Attia A, Dayan S. Global overview of imitation learning. arXiv preprint arXiv: 1801.06503, 2018.
[71]	Hester T, Vecerik M, Pietquin O, Lanctot M, Schaul T, Piot B, et al. Deep Q-learning from demonstrations. arXiv preprint arXiv: 1704.03732, 2017.
[72]	Vecerik M, Hester T, Scholz J, Wang F M, Pietquin O, Piot B, et al. Leveraging demonstrations for deep reinforcement learning on robotics problems with sparse rewards. arXiv preprint arXiv: 1707.08817, 2017.
[73]	Guillen-Perez A, Cano M. Learning from Oracle demonstrations — a new approach to develop autonomous intersection management control algorithms based on multiagent deep reinforcement learning. IEEE Access, 2022, 10: 53601-53613 doi: 10.1109/ACCESS.2022.3175493
[74]	Huang Z Y, Wu J D, Lv C. Efficient deep reinforcement learning with imitative expert priors for autonomous driving. IEEE Transactions on Neural Networks and Learning Systems, DOI: 10.1109/TNNLS.2022.3142822
[75]	Hu Z J, Wan K F, Gao X G, Zhai Y W, Wang Q L. Deep reinforcement learning approach with multiple experience pools for UAV's autonomous motion planning in complex unknown environments. Sensors, 2020, 20(7): Article No. 1890 doi: 10.3390/s20071890
[76]	Wan K F, Wu D W, Li B, Gao X G, Hu Z J, Chen D Q. ME-MADDPG: An efficient learning-based motion planning method for multiple agents in complex environments. International Journal of Intelligent Systems, 2022, 37(3): 2393-2427 doi: 10.1002/int.22778
[77]	Lowe R, Wu Y, Tamar A, Harb J, Abbeel P, Mordatch I. Multi-agent actor-critic for mixed cooperative-competitive environments. In: Proceedings of the 31st International Conference on Neural Information Processing Systems. Long Beach, CA, USA: Curran Associates Inc., 2017. 6382−6393
[78]	Zhang T Z, Miao X H, Li Y B, Jia L, Zhuang Y H. AUV surfacing control with adversarial attack against DLaaS framework. IEEE Transactions on Computers, DOI: 10.1109/TC.2021.3072072
[79]	Sutton R S. Integrated architectures for learning, planning, and reacting based on approximating dynamic programming. In: Proceedings of the 7th International Conference on Machine Learning (ICML). Austin, Texas, USA: ACM, 1990. 216−224
[80]	Silver D, Sutton R S, Müller M. Sample-based learning and search with permanent and transient memories. In: Proceedings of the 25th International Conference on Machine Learning (ICML). Helsinki, Finland: ACM, 2008. 968−975
[81]	Santos M, Jose A, Lopez V, Botella G. Dyna-H: A heuristic planning reinforcement learning algorithm applied to role-playing-game strategy decision systems. Knowledge-Based Systems, 2012, 32: 28-36 doi: 10.1016/j.knosys.2011.09.008
[82]	Pan Y C, Yao H S, Farahmand A, White M. Hill climbing on value estimates for search-control in Dyna. In: Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI). Macao, China: AAAI Press, 2019. 3209−3215
[83]	Pan Y C, Zaheer M, White A, Patterson A, White M. Organizing experience: A deeper look at replay mechanisms for sample-based planning in continuous state domains. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI). Stockholm, Sweden: AAAI Press, 2018. 4794−4800
[84]	Andrychowicz M, Wolski F, Ray A, Schneider J, Fong R, Welinder P, et al. Hindsight experience replay. In: Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS). Long Beach, CA, USA: Curran Associates Inc., 2017. 5055–5065
[85]	Schaul T, Horgan D, Gregor K, Silver D. Universal value function approximators. In: Proceedings of the 32nd International Conference on Machine Learning (ICML). Lille, France: JMLR.org, 2015. 1312−1320
[86]	Luu T M, Yoo C D. Hindsight goal ranking on replay buffer for sparse reward environment. IEEE Access, 2021, 9: 51996-52007 doi: 10.1109/ACCESS.2021.3069975
[87]	Fang M, Zhou C, Shi B, Gong B Q, Xu J, Zhang T. DHER: Hindsight experience replay for dynamic goals. In: Proceedings of the 7th International Conference on Learning Representations (ICLR). New Orleans, LA, USA: OpenReview.net, 2019. 1−12
[88]	Hu Z J, Gao X G, Wan K F, Evgeny N, Li J L. Imaginary filtered hindsight experience replay for UAV tracking dynamic targets in large-scale unknown environments. Chinese Journal of Aeronautics, DOI: 10.1016/j.cja.2022.09.008
[89]	Fang M, Zhou T Y, Du Y L, Han L, Zhang Z Y. Curriculum-guided hindsight experience replay. In: Proceedings of the 33rd International Conference on Neural Information Processing Systems (NIPS). Vancouver, BC, Canada: MIT Press, 2019. 12623−12634
[90]	Yang R, Fang M, Han L, Du Y L, Luo F, Li X. MHER: Model-based hindsight experience replay. arXiv preprint arXiv: 2107.00306, 2021.