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BL-WoLF: A Framework For Loss-Bounded Learnability In Zero-Sum Games

机译:BL-WoLF:零和游戏中损失受限的可学习性的框架

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We present BL-WoLF, a framework for leam-ability in repeated zero-sum games where the cost of learning is measured by the losses the learning agent accrues (rather than the number of rounds). The game is adversarially chosen from some family that the learner knows. The opponent knows the game and the learner's learning strategy. The learner tries to either not accrue losses, or to quickly learn about the game so as to avoid future losses (this is consistent with the Win or Learn Fast (WoLF) principle; BL stands for "bounded loss"). Our framework allows for both probabilistic and approximate learning. The resultant notion of BL-WoLF-leamability can be applied to any class of games, and allows us to measure the inherent disadvantage to a player that does not know which game in the class it is in. We present guaranteed BL-WoLF-learnability results for families of games with deterministic payoffs and families of games with stochastic payoffs. We demonstrate that these families are guaranteed approximately BL-WoLF-learnable with lower cost. We then demonstrate families of games (both stochastic and deterministic) that are not guaranteed BL-WoLF-learnable. We show that those families, nevertheless, are BL-WoLF-learnable. To prove these results, we use a key lemma which we derive.
机译:我们提出了BL-WoLF,这是重复的零和游戏的学习能力框架,其中学习成本是根据学习代理人的损失(而不是回合数)来衡量的。对抗性地从学习者知道的某个家庭中选择游戏。对手知道游戏和学习者的学习策略。学习者尝试要么不产生损失,要么快速学习游戏,以避免将来遭受损失(这与“赢或学得快(WoLF)”原则一致; BL代表“有界损失”)。我们的框架允许概率学习和近似学习。由此产生的BL-WoLF可学习性概念可以应用于任何类型的游戏,并且使我们能够衡量不知道该类属于哪款游戏的玩家的固有劣势。我们提供保证的BL-WoLF可学习性具有确定性收益的游戏族和具有随机收益的游戏族的结果。我们证明,这些家庭可以保证以较低的成本获得大约BL-WoLF可学习的知识。然后,我们演示了不能保证BL-WoLF可学习的游戏家族(随机的和确定性的)。我们表明,尽管如此,这些家庭还是可以通过BL-WoLF学习的。为了证明这些结果,我们使用导出的关键引理。

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