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First explore the nodes A,B,C once. For reference see this paper by David Silver and Sylvain Gelly, Combining Online and Offline Knowledge in UCT If any action from the current state $s$ is not represented in the tree, $\exists a \in \mathcal{A}(s),(s, a) \notin \mathcal{T},$ then the uniform random policy $\pi_{\text {random }}$ is used to select an action ...


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If the initial state is not always the same, but if your agent is allowed to observe what the initial state is before it has to start running the search algorithm, there's basically no problem; it has all the information it needs when it starts running the tree search. This is how we typically use MCTS (or any other tree searches): we first observe what the ...


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Assigning a value of $\infty$ to unvisited nodes is indeed the "default" or most basic choice, and it indeed ensures that the search never visits a node for a second time if it also still has siblings that have not had any visits. But many other kinds of values have been tried in the literature too. Gelly and Wang, in "Exploration exploitation ...


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