Discretization of Continuous Action Spaces in Extensive-Form Games

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Discretization of Continuous Action Spaces in Extensive-Form Games
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
Added 16 Apr 2016
Updated 16 Apr 2016
Type Journal
Year 2015
Where ATAL
Authors Christian Kroer, Tuomas Sandholm
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