{"id":159412,"date":"2010-05-01T00:00:00","date_gmt":"2010-05-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/coherent-inference-on-optimal-play-in-game-trees\/"},"modified":"2018-10-16T21:58:00","modified_gmt":"2018-10-17T04:58:00","slug":"coherent-inference-on-optimal-play-in-game-trees","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/coherent-inference-on-optimal-play-in-game-trees\/","title":{"rendered":"Coherent Inference on Optimal Play in Game Trees"},"content":{"rendered":"<div class=\"asset-content\">\n<p>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.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>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 [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Proceedings of the Thirteenth Conference on Artificial Intelligence and Statistics AISTATS 2010 (to appear)","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Proceedings of the Thirteenth Conference on Artificial Intelligence and Statistics AISTATS 2010 (to 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