Multiple Policy Value Monte Carlo Tree Search
  Many of the strongest game playing programs use a combination of Monte Carlo
tree search (MCTS) and deep neural networks (DNN), where the DNNs are used as
policy or value evaluators. Given a limited budget, such as online playing or
during the self-play phase of AlphaZero (AZ) training, a balance needs to be
reached between accurate state estimation and more MCTS simulations, both of
which are critical for a strong game playing agent. Typically, larger DNNs are
better at generalization and accurate evaluation, while smaller DNNs are less
costly, and therefore can lead to more MCTS simulations and bigger search trees
with the same budget. This paper introduces a new method called the multiple
policy value MCTS (MPV-MCTS), which combines multiple policy value neural
networks (PV-NNs) of various sizes to retain advantages of each network, where
two PV-NNs f_S and f_L are used in this paper. We show through experiments on
the game NoGo that a combined f_S and f_L MPV-MCTS outperforms single PV-NN
with policy value MCTS, called PV-MCTS. Additionally, MPV-MCTS also outperforms
PV-MCTS for AZ training.
