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 cs-677sp2010:decision-theoretic-graphical-models [2014/12/09 09:57]ryancha created cs-677sp2010:decision-theoretic-graphical-models [2014/12/12 11:29] (current)ryancha 2014/12/12 11:29 ryancha 2014/12/09 09:57 ryancha created 2014/12/12 11:29 ryancha 2014/12/09 09:57 ryancha created Line 18: Line 18: A decision tree has two types of nodes, both of which fittingly represent ''​decisions'':​ A decision tree has two types of nodes, both of which fittingly represent ''​decisions'':​ - [[File:​Oil_decision_tree.png|frame|The oil well example encoded as a decision tree]] [[File:​Decision_tree_agent_node.png]] Agent nodes represent the decisions of an agent. Their outbound edges represent the possible choices of the agent. The root of the tree is an agent node, reflecting the fact that while the decision tree paradigm does model the world it is ultimately focused on determining optimal agent actions. + [[media:​cs-677sp10:​Oil_decision_tree.png|frame|The oil well example encoded as a decision tree]] [[media:​cs-677sp10:​Decision_tree_agent_node.png]] Agent nodes represent the decisions of an agent. Their outbound edges represent the possible choices of the agent. The root of the tree is an agent node, reflecting the fact that while the decision tree paradigm does model the world it is ultimately focused on determining optimal agent actions. - [[File:​Decision_tree_nature_node.png]] Nature nodes represent the decisions of nature -- in other words, the outcomes of random processes not under the agent'​s control. Their outbound edges represent the possible values of a random variable and are labeled with the probabilities of those outcomes. + [[media:​cs-677sp10:​Decision_tree_nature_node.png]] Nature nodes represent the decisions of nature -- in other words, the outcomes of random processes not under the agent'​s control. Their outbound edges represent the possible values of a random variable and are labeled with the probabilities of those outcomes. Each node is labeled with the utility at that state in the decision process, and the outgoing edges of terminal nodes are simply drawn pointing to a number representing the final utility. The optimal decision on an agent node can be marked using a bolded edge. Each node is labeled with the utility at that state in the decision process, and the outgoing edges of terminal nodes are simply drawn pointing to a number representing the final utility. The optimal decision on an agent node can be marked using a bolded edge. Line 37: Line 37: [[Image:​Influence_diagram_utility_node.png]] Let $\,\!U$ be a set of utility variables. For all $\,\!u \in U$, there exists a deterministic utility function $\,\!f_{u} : \bigotimes_{p \in Parents(u)} Values(p) : \mathfrak{R}$ (where we interpret $\,​\!\bigotimes$ as a cumulative cartesian product), and $\,​\!Children(u)=\emptyset$ [[Image:​Influence_diagram_utility_node.png]] Let $\,\!U$ be a set of utility variables. For all $\,\!u \in U$, there exists a deterministic utility function $\,\!f_{u} : \bigotimes_{p \in Parents(u)} Values(p) : \mathfrak{R}$ (where we interpret $\,​\!\bigotimes$ as a cumulative cartesian product), and $\,​\!Children(u)=\emptyset$ - [[File:​Oil_influence_diagram.png|frame|An influence diagram encoding of the oil scenario including the oil test. Note that the cost of the test is now separated from the benefit of striking oil.]] + [[media:​cs-677sp10:​Oil_influence_diagram.png|frame|An influence diagram encoding of the oil scenario including the oil test. Note that the cost of the test is now separated from the benefit of striking oil.]] ===Computing Maximum Expected Utility=== ===Computing Maximum Expected Utility=== Line 58: Line 58: ====A==== ====A==== - [[File:​Oil_with_test_decision_tree.png|800px]] + [[media:​cs-677sp10:​Oil_with_test_decision_tree.png|800px]] The test should not be performed. The test should not be performed. <​nowiki>​[Note:​ why is this not breaking even as the original example suggests it should?​]​ <​nowiki>​[Note:​ why is this not breaking even as the original example suggests it should?​] 