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@jemoka / Jemoka Knowledge Base / wiki/concepts/maxq.md
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--- title: "MaxQ" type: concept related: [Maxq, Markov Decision Process] source: https://www.jemoka.com/posts/kbhmaxq/ confidence: high status: active --- Two Abstractions “temporal abstractions”: making decisions without consideration / abstracting away time (MDP) “state abstractions”: making decisions about groups of states at once Graph MaxQ formulates a policy as a graph, which formulates a set of \(n\) policies Max Node This is a “policy node”, connected to a series of \(Q\) nodes from which it takes the max and propegate down. If we are at a leaf max-node, the actual action is taken and control is passed back t to the top of the graph Q Node each node computes \(Q(S,A)\) for a value at that action Hierachical Value Function \begin{equation} Q(s,a) = V_{a}(s) + C_{i}(s,a) \end{equation} the value function of the root node is the value obtained over all nodes in the graph where: \begin{equation} C_{i}(s,a) = \sum_{s’}^{} P(s’|s,a) V(s’) \end{equation} Learning MaxQ maintain two tables \(C_{i}\) and \(\tilde{C}_{i}(s,a)\) (which is a special completion function which corresponds to a special reward \(\tilde{R}\) which prevents the model from doing egregious ending actions) choose \(a\) according to exploration strategy execute \(a\), observe \(s’\), and compute \(R(s’|s,a)\) Then, update: