基于专家博弈集成的非平稳未知零和博弈的有效情景学习
Efficient Episodic Learning of Nonstationary and Unknown Zero-Sum Games Using Expert Game Ensembles
摘要：
博弈论为战略互动的许多应用提供了必要的分析。然而，如何构建一个游戏模型，什么是它的保真度的问题很少被解决。在这项工作中，我们考虑学习一类重复的零和游戏未知，时变的回报矩阵，和噪声反馈，通过使用一个合奏的基准游戏模型。这些模型可以在连续播放期间进行预训练和动态收集。它们作为先验边信息，不完全地支撑未知的真实博弈模型。我们提出了OFULinMat，一个情景学习算法，它集成了自适应估计的游戏模型和学习的战略。所提出的算法实现了鞍点遗憾的次线性界。通过理论分析和数值算例证明了该算法的有效性。我们使用一个动态蜜罐分配游戏作为案例研究来说明和证实我们的结果。我们还讨论了我们的框架和经典的对抗性多臂强盗框架之间的关系和突出的区别。
英文摘要：
Game theory provides essential analysis in many applications of strategic interactions. However, the question of how to construct a game model and what is its fidelity is seldom addressed. In this work, we consider learning in a class of repeated zero-sum games with unknown, time-varying payoff matrix, and noisy feedbacks, by making use of an ensemble of benchmark game models. These models can be pre-trained and collected dynamically during sequential plays. They serve as prior side information and imperfectly underpin the unknown true game model. We propose OFULinMat, an episodic learning algorithm that integrates the adaptive estimation of game models and the learning of the strategies. The proposed algorithm is shown to achieve a sublinear bound on the saddle-point regret. We show that this algorithm is provably efficient through both theoretical analysis and numerical examples. We use a dynamic honeypot allocation game as a case study to illustrate and corroborate our results. We also discuss the relationship and highlight the difference between our framework and the classical adversarial multi-armed bandit framework.
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