Discretization of Continuous Action Spaces in Extensive-Form Games

8 years 10 days ago

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Extensive-form games are a powerful tool for modeling a large range of multiagent scenarios. However, most solution algorithms require discrete, ﬁnite games. In contrast, many real-world domains require modeling with continuous action spaces. This is usually handled by heuristically discretizing the continuous action space without solution quality bounds. In this paper we address this issue. Leveraging esults on abstraction solution quality, we develop the ﬁrst framework for providing bounds on solution quality for discretization of continuous action spaces in extensive-form games. For games where the error is Lipschitz-continuous in the distance of a continuous point to its nearest discrete point, we show that a uniform discretization of the space is optimal. When the error is monotonically increasing in distance to nearest discrete point, we develop an integer program for ﬁnding the optimal discretization when the error is described by piecewise linear functions. This result c...

Christian Kroer, Tuomas Sandholm

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