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Conference Paper

Coherent Inference on Optimal Play in Game Trees


Hennig,  P
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Hennig, P., Stern, D., & Graepel, T. (2010). Coherent Inference on Optimal Play in Game Trees. In JMLR Workshop and Conference Proceedings Volume 9: AISTATS 2010 (pp. 326-333). Cambridge, MA, USA: JMLR.

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Round-based games are an instance of discrete planning problems. Some of the best contemporary game tree search algorithms use random roll-outs as data. Relying on a good policy, they learn on-policy values by propagating information upwards in the tree, but not between sibling nodes. Here, we present a generative model and a corresponding approximate message passing scheme for inference on the optimal, off-policy value of nodes in smooth AND/OR trees, given random roll-outs. The crucial insight is that the distribution of values in game trees is not completely arbitrary. We define a generative model of the on-policy values using a latent score for each state, representing the value under the random roll-out policy. Inference on the values under the optimal policy separates into an inductive, pre-data step and a deductive, post-data part. Both can be solved approximately with Expectation Propagation, allowing off-policy value inference for any node in the (exponentially big) tree in linear time.