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Could a better algorithm other than Monte Carlo be used for the AlphaGo computer? Why didn't the DeepMind team think of choosing another kind of algorithm rather than spending time on their neural nets?

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The paper that introduced AlphaGo, Mastering the game of Go with deep neural networks and tree search, motivates the use of MCTS

Monte Carlo tree search (MCTS) uses Monte Carlo rollouts to estimate the value of each state in a search tree. As more simulations are executed, the search tree grows larger and the relevant values become more accurate. The policy used to select actions during search is also improved over time, by selecting children with higher values. Asymptotically, this policy converges to optimal play, and the evaluations converge to the optimal value function. The strongest current Go programs are based on MCTS, enhanced by policies that are trained to predict human expert moves. These policies are used to narrow the search to a beam of high-probability actions, and to sample actions during rollouts. This approach has achieved strong amateur play.

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