一种用于两人零和博弈对手适应的元策略演化学习算法

吴哲; 李凯; 徐航; 兴军亮

doi:10.16383/j.aas.c211003

一种用于两人零和博弈对手适应的元策略演化学习算法

doi: 10.16383/j.aas.c211003

吴哲^{1, 2,},
李凯^{1, 2,},
徐航^{1, 2,},
兴军亮^{1, 2, 3,}

1.
中国科学院自动化研究所智能系统与工程研究中心北京 100190
2.
中国科学院大学人工智能学院北京 100049
3.
清华大学计算机科学与技术系北京 100084

基金项目: 国家重点研发计划(2020AAA0103401), 国家自然科学基金(62076238, 61902402), 中国科学院战略性先导研究项目(XDA27000000), CCF-腾讯犀牛鸟基金(RAGR20200104)资助

详细信息

作者简介:
吴哲：中国科学院自动化研究所智能系统与工程研究中心硕士研究生. 2019年获得山东大学工学学士学位. 主要研究方向为计算机博弈, 强化学习. E-mail: wuzhe2019@ia.ac.cn

李凯：中国科学院自动化研究所智能系统与工程研究中心副研究员. 2018年获得中国科学院自动化研究所模式识别与智能系统博士学位. 主要研究方向为计算机博弈, 强化学习. E-mail: kai.li@ia.ac.cn

徐航：中国科学院自动化研究所智能系统与工程研究中心硕士研究生. 2020年获得武汉大学工学学士学位. 主要研究方向为计算机博弈, 强化学习. E-mail: xuhang2020@ia.ac.cn

兴军亮：清华大学计算机科学与技术系研究员. 2012年获得清华大学计算机科学与技术系博士学位. 主要研究方向为计算机博弈. 本文通信作者. E-mail: jlxing@nlpr.ia.ac.cn

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出版历程
- 收稿日期: 2021-10-22
- 录用日期: 2022-03-14
- 网络出版日期: 2022-05-05
- 刊出日期: 2022-10-14

A Meta-evolutionary Learning Algorithm for Opponent Adaptation in Two-player Zero-sum Games

WU Zhe^{1, 2
,},
LI Kai^{1, 2
,},
XU Hang^{1, 2
,},
XING Jun-Liang^{1, 2, 3
,}

1.
Center for Research on Intelligent System and Engineering, Institute of Automation, Chinese Academy of Sciences, Beijing 100190
2.
School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049
3.
Department of Computer Science and Technology, Tsinghua University, Beijing 100084

Funds: Supported by National Key Research and Development Program of China (2020AAA0103401), National Natural Science Foundation of China (62076238, 61902402), Strategic Priority Research Program of Chinese Academy of Sciences (XDA27000000), and CCF-Tencent Open Research Fund (RAGR20200104)

More Information

Author Bio:
WU Zhe　Master student at the Center for Research on Intelligent System and Engineering, Institute of Automation, Chinese Academy of Sciences. He received his bachelor degree in engineering from Shandong University in 2019. His research interest covers computer game and reinforcement learning

LI Kai　Associate professor at the Center for Research on Intelligent System and Engineering, Institute of Automation, Chinese Academy of Sciences. He received his Ph.D. degree in pattern recognition and intelligent system from Institute of Automation, Chinese Academy of Sciences in 2018. His research interest covers computer game and reinforcement learning

XU Hang　Master student at the Center for Research on Intelligent System and Engineering, Institute of Automation, Chinese Academy of Sciences. He received his bachelor degree in engineering from Wuhan University in 2020. His research interest covers computer game and reinforcement learning

XING Jun-Liang　Professor in the Department of Computer Science and Technology, Tsinghua University. He received his Ph.D. degree in Department of Computer Science and Technology from Tsinghua University in 2012. His main research interest is computer game. Corresponding author of this paper

摘要

摘要: 围绕两人零和博弈所开展的一系列研究, 近年来在围棋、德州扑克等问题中取得了里程碑式的突破. 现有的两人零和博弈求解方案大多在理性对手的假设下围绕纳什均衡解开展, 是一种力求不败的保守型策略, 但在实际博弈中由于对手非理性等原因并不能保证收益最大化. 对手建模为最大化博弈收益提供了一种新途径, 但仍存在建模困难等问题. 结合元学习的思想提出了一种能够快速适应对手策略的元策略演化学习求解框架. 在训练阶段, 首先通过种群演化的方法不断生成风格多样化的博弈对手作为训练数据, 然后利用元策略更新方法来调整元模型的网络权重, 使其获得快速适应的能力. 在Leduc扑克、两人有限注德州扑克(Heads-up limit Texas Hold＇em, LHE)和RoboSumo上的大量实验结果表明, 该算法能够有效克服现有方法的弊端, 实现针对未知风格对手的快速适应, 从而为两人零和博弈收益最大化求解提供了一种新思路.
- 两人零和博弈 /
- 纳什均衡 /
- 对手建模 /
- 元学习 /
- 种群演化
Abstract: Recently, two-player zero-sum games have made impressive breakthroughs in the Go and Texas Hold＇em. Most of the existing two-player zero-sum game solutions are based on the assumption of rational opponents to approximate the Nash equilibrium solutions, which is a conservative strategy of trying to be undefeated but does not guarantee maximum payoffs in practice due to the opponents＇ irrationality. The opponent modeling provides a new way to maximize the payoff, but modeling has difficulties. This paper proposes a meta-evolutionary learning framework that can quickly adapt to the opponents. In the training phase, we first generate opponents with different styles as training data through the population evolution method, and then use the meta-strategy update method to adjust the network weights of the meta-model so that it can gain the ability to adapt quickly. Extensive experiments on Leduc poker, heads-up limit Texas Hold＇em (LHE), and RoboSumo have shown that the algorithm can effectively overcome the drawbacks of existing methods and achieve fast adaptation to unknown style of opponents, thus providing a new way of solving two-player zero-sum games with maximum payoff.
- Two-player zero-sum games /
- Nash equilibrium /
- opponent modeling /
- meta learning /
- population evolution

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图 1 本文提出的元模型训练方法

Fig. 1 The meta-model＇s training process

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图 2 本文算法与基线算法在RoboSumo中的对比

Fig. 2 Comparison of our method with the baseline algorithm in RoboSumo

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图 3 消融实验

Fig. 3 Ablation study

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图 5 超参数设置对模型性能影响

Fig. 5 Effect of hyperparameter settings

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图 4 种群演化模块生成的对手策略

Fig. 4 Visualization of the styles of the strategies

下载: 全尺寸图片幻灯片

表 1 不同环境下的实验参数设置

Table 1 Hyperparameters settings

参数	Leduc	LHE	RoboSumo
状态空间	36	72	120
动作空间	4	4	8
网络尺寸	[64, 64]	[128, 128]	[128, 128]
训练步长$\alpha$	0.100	0.050	0.003
训练步长$\beta$	0.0100	0.0100	0.0006
折扣系数$\gamma$	0.990	0.995	0.995
梯度更新步数	1	1	1
种群规模	10	10	10
精英比例$\vartheta$	0.2	0.4	0.4
变异率	0.3	0.1	0.2
变异强度	0.1	0.1	0.1
测试更新步长	0.100	0.050	0.001
测试更新步数	3	3	3
评估局数	50	100	50
存储资源 (GB)	~ 0.3	~ 2.0	~ 1.5
迭代次数 (T)	100	400	300

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表 2 本文算法与基线算法在Leduc环境中的对比

Table 2 The average return of our method and baseline methods in Leduc

方法	Random 对手	Call 对手	Bluff 对手	CFR 对手	NFSP 对手
本文算法	1.359 ± 0.023	0.646 ± 0.069	0.576 ± 0.043	− 0.162 ± 0.032	0.325 ± 0.096
CFR 算法	0.749 ± 0.014	0.364 ± 0.010	0.283 ± 0.028	0.010 ± 0.024	0.144 ± 0.007
DRON 算法	1.323 ± 0.014	0.418 ± 0.011	0.409 ± 0.052	− 0.347 ± 0.031	0.212 ± 0.080
EOM 算法	1.348 ± 0.015	0.635 ± 0.007	0.444 ± 0.024	− 0.270 ± 0.042	− 0.012 ± 0.023
NFSP 算法	0.780 ± 0.019	0.132 ± 0.024	0.029 ± 0.022	− 0.412 ± 0.040	0.011 ± 0.027
MAML 算法	1.372 ± 0.028	0.328 ± 0.013	0.323 ± 0.044	− 0.409 ± 0.010	0.089 ± 0.051
本文算法 +PPO	1.353 ± 0.011	0.658 ± 0.005	0.555 ± 0.017	− 0.159 ± 0.041	0.314 ± 0.012
本文算法 −EA	0.994 ± 0.042	0.611 ± 0.021	0.472 ± 0.038	− 0.224 ± 0.016	0.203 ± 0.029
EA 算法	0.535 ± 0.164	0.422 ± 0.108	0.366 ± 0.113	− 0.365 ± 0.094	0.189 ± 0.102
Oracle	1.373 ± 0.007	0.662 ± 0.014	0.727 ± 0.012	− 0.089 ± 0.016	0.338 ± 0.041

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表 3 本文算法与基线算法在LHE环境中的对比

Table 3 The average return of our method and baseline methods in LHE

方法	Random 对手	LA 对手	TA 对手	LP 对手
本文算法	2.594 ± 0.089	0.335 ± 0.012	0.514 ± 0.031	0.243 ± 0.102
DRON 算法	2.131 ± 0.672	− 0.609 ± 0.176	0.294 ± 0.057	0.022 ± 0.028
EOM 算法	2.555 ± 0.020	− 0.014 ± 0.013	0.237 ± 0.023	0.144 ± 0.128
NFSP 算法	1.342 ± 0.033	− 0.947 ± 0.012	− 0.352 ± 0.094	0.203 ± 0.089
MAML 算法	2.633 ± 0.035	0.037 ± 0.047	0.231 ± 0.057	0.089 ± 0.051
本文算法 +PPO	2.612 ± 0.058	0.327 ± 0.011	0.478 ± 0.042	0.246 ± 0.070
本文算法 −EA	2.362 ± 0.023	0.185 ± 0.049	0.388 ± 0.012	0.119 ± 0.015
EA 算法	2.193 ± 0.158	0.096 ± 0.087	0.232 ± 0.097	0.091 ± 0.009
Oracle	2.682 ± 0.033	0.513 ± 0.009	0.624 ± 0.011	0.270 ± 0.026

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