Doing Better Than UCT: Rational Monte Carlo Sampling in Trees
  UCT, a state-of-the art algorithm for Monte Carlo tree sampling (MCTS), is
based on UCB, a sampling policy for the Multi-armed Bandit Problem (MAB) that
minimizes the accumulated regret. However, MCTS differs from MAB in that only
the final choice, rather than all arm pulls, brings a reward, that is, the
simple regret, as opposite to the cumulative regret, must be minimized. This
ongoing work aims at applying meta-reasoning techniques to MCTS, which is
non-trivial. We begin by introducing policies for multi-armed bandits with
lower simple regret than UCB, and an algorithm for MCTS which combines
cumulative and simple regret minimization and outperforms UCT. We also develop
a sampling scheme loosely based on a myopic version of perfect value of
information. Finite-time and asymptotic analysis of the policies is provided,
and the algorithms are compared empirically.
