  This paper makes two proposals for Monte Carlo Softmax Search, which is a
recently proposed method that is classified as a selective search like the
Monte Carlo Tree Search. The first proposal separately defines the
node-selection and backup policies to allow researchers to freely design a
node-selection policy based on their searching strategies and confirms the
principal variation produced by the Monte Carlo Softmax Search to that produced
by a minimax search. The second proposal modifies commonly used learning
methods for positional evaluation functions. In our new proposals, evaluation
functions are learned by Monte Carlo sampling, which is performed with the
backup policy in the search tree produced by Monte Carlo Softmax Search. The
learning methods under consideration include supervised learning, reinforcement
learning, regression learning, and search bootstrapping. Our sampling-based
learning not only uses current positions and principal variations but also the
internal nodes and important variations of a search tree. This step reduces the
number of games necessary for learning. New learning rules are derived for
sampling-based learning based on the Monte Carlo Softmax Search and
combinations of the modified learning methods are also proposed in this paper.
