>That's what the simple math says, but the complex math says that UCT is >asymptotically optimal!
is there a proof for UCT? I just know UCB is aymptotically optimal for the bandit problem. Actually, what is the regret function for UCT? >Increasing speed improves the outcome in two ways. First, you have more time >to examine the better moves more deeply. Second, you can expand more moves >at each node. > >A third potential advantage is to keep the tree the same size and do better >analysis. That is, use the speed to reduce the error rate. If this is done >by having heavy knowledge then the solution is not scalable. But you can >also create online learning algorithms that improve analysis, which could be >scalable. Can we say, searching in larger tree is ONLY for reducing the error rate of the upper layers of the whole searching tree? Here, the upper layer portion of the searching tree is a small subtree with fixed size. To its extreme, there is only one layer in the "upper layer subtree", in that case we just do some playouts on each move of the current position and pick the best one. Any further tree extension can be seen as "searching in the larger part of the tree for reducing error rates in the first layer".
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