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摘要: 以德州扑克游戏为代表的大规模不完美信息博弈是现实世界中常见的一种博弈类型. 现有以求解纳什均衡策略为目标的主流德州扑克求解算法存在依赖博弈树模型、算力消耗大、策略过于保守等问题, 导致智能体在面对不同对手时无法最大化自身收益. 为解决上述问题, 提出一种轻量高效且能快速适应对手策略变化进而剥削对手的不完美信息博弈求解框架. 本框架分为智能体离线训练和在线博弈两个阶段. 第1阶段基于演化学习思想训练智能体, 得到能够剥削不同博弈风格对手的策略神经网络. 在第2博弈阶段中, 智能体在线建模并适应未知风格对手, 利用种群策略集成的方法最大化剥削对手. 在两人无限注德州扑克环境中的实验结果表明, 本框架在面对动态对手策略时, 相比已有方法能够大幅提升博弈性能.Abstract: Texas Hold＇em is a typical large-scale imperfect information game in the real world. Existing algorithms computing Nash equilibriums in the Texas Hold＇em have severe problems, including the heavy dependency on the game＇s abstract model, the considerable resource consumption, and the learned strategy＇s conservatism prevents it from maximizing the payoffs when facing different opponents. To alleviate these problems, we propose a light-weight and efficient framework for imperfect information that can quickly adapt to new opponents/strategies. It consists of two stages: The offline training stage and the online game stage. Based on the evolutionary theory, we train policy networks to exploit opponents with distinct styles in the training stage. While during the game stage, the agent first models the unknown opponent and then weighs the trained policies to integrate an adaptive strategy, which maximizes the exploitation of the opponent. Experimental results in heads-up no-limit Texas Hold＇em show the superiority of the proposed framework. Strategy obtained by this framework significantly outperforms the existing methods when facing dynamic opponents.1) 1
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图 2 不完美信息博弈求解框架整体流程
Fig. 2 Overall process of the imperfect information game solving framework
图 8 策略输出网络隐含层神经元数量对种群平均适应度的影响
Fig. 8 The influence of the hidden neurons in policy output network on population fitness
图 9 种群生存率对种群平均适应度的影响
Fig. 9 The influence of population survival rates on population average fitness
图 10 不同训练策略对种群平均适应度的影响
Fig. 10 The influence of different training strategies on population average fitness
表 1 对手智能体博弈风格及定义
Table 1 The opponents＇play styles and definitions
名称 类型 手牌松紧度 策略激进度 ${O_{\rm{1}}}$ 松−弱 70 % 极度保守 ${O_2}$ 松−凶 70 % 极度激进 ${O_3}$ 紧−弱 10 % 极度保守 ${O_4}$ 紧−凶 10 % 极度激进 ${O_5}$ 松−弱 50 % 相对保守 ${O_6}$ 松−凶 50 % 相对激进 ${O_7}$ 紧−弱 30 % 相对保守 ${O_8}$ 紧−凶 30 % 相对激进 
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表 2 策略网络结构与训练参数
Table 2 Policy network structure and the training hyper-parameters
参数含义 参数值 对手特征网络LSTM区块数 5 对手特征网络LSTM时间序列步数 5 对手特征网络输出维度 200 游戏特征网络LSTM区块数 5 游戏特征网络LSTM时间序列步数 5 游戏特征网络输出维度 300 策略输出网络输入层神经元数量 500 策略输出网络隐含层数量 2 策略输出网络隐含层神经元数量 300 策略输出网络输出层神经元数量 10 种群演化代数 300 种群个体规模 100 种群生存率 0.25 基因变异率(初始/最终) 0.25/0.05 基因变异强度(初始/最终) 0.5/0.1 单个对手对打训练牌局数量 10000 对手特征库收集游戏对打局数 100000
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表 3 消融实验结果(mbb/h)
Table 3 Ablation study results (mbb/h)
智能体\对手 ${O_{\rm{1}}}$ ${O_2}$ ${O_3}$ ${O_4}$ ${O_5}$ ${O_6}$ ${O_7}$ ${O_8}$ ${O_{random}}$ Slumbot 702.53 12761 4942.58 14983 652.73 2623.14 484.29 2449.08 3387.13 ${A_{tar}}$ 999.92 29232 1494.92 27474 1391.04 12746 1371.10 34546 — ${A_{base}}$ 1000.00 22611 1205.05 20380 1109.84 9892.43 793.42 14568 5105.38 ${A_{ave}}$ 999.91 78.46 34.06 −5537.19 927.84 92.36 −631.55 −4461.82 −1068.44 ${A_{\rm{int} }}$ 999.92 29964 1305.04 27314 1316.21 12874 1380.88 18330 2738.98 ${A^*}$ 1000.00 24888 1310.34 27526 1286.08 11253 1020.38 16514 6359.36
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表 4 博弈性能对比结果(mbb/h)
Table 4 Performance comparison results (mbb/h)
智能体 ${A^*}$ ASHE Slumbot Deepstack NFSP 知识AI ${O_{random}}$ ${A^*}$ — 675.68 −48.49 −896.76 32255 229.64 6359.36 ASHE −675.68 — −153.35 −1552.64 11904 −13.00 3177.68 Slumbot 48.49 153.35 — −103.44 8623.18 52.43 3387.13 DeepStack 896.76 1552.64 103.44 — 4084.27 139.41 1791.27 NFSP −32255 −11904 −8623.18 −4084.27 — −3257.75 −18819 知识AI −229.64 13.00 −52.43 −139.41 3257.75 — −91.92 ${O_{random}}$ −6859.36 −3177.68 −3387.13 −1791.27 18819 91.92 —
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表 5 算法轻量性对比
Table 5 Light-weight comparison
智能体 训练阶段资源需求 测评阶段资源需求 存储资源(GB) 计算资源(h) 存储资源(GB) 计算资源(h) 响应时间(s) ${A^*}$ ~30 ~2×103 CPU <0.5 <0.1 CPU <0.1 ASHE ~30 ~103 CPU ~30 <0.1 CPU <0.1 Slumbot >500 >105 CPU >500 >10 CPU ~1 DeepStack >500 >106 CPU
>103 GPU>10 ~103 CPU
~103 GPU~30 NFSP >50 ~104 CPU
~102 GPU~1 <1 CPU
<1 GPU<1 人类玩家 — — — — ~15
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