  A recent theoretical analysis of a corrected-version of a Monte-Carlo tree
search (MCTS) method, so-called UCT, established an unexpected result, due to a
great deal of empirical successes reported from heuristic usage of UCT with
relevant adjustments for the problem domains in the literature, that its
convergence rate in estimating the expected error relative to the optimal value
of a finite-horizon Markov decision process (MDP) at an initial state is
polynomial. We strengthen this dispiriting slow-convergence result by arguing
within a simpler framework in the perspective of MDP, apart from the usual MCTS
description, that just simpler UCB1 applied with the policy set as the arm set
is actually competitive with or asymptotically faster than the
corrected-version of UCT because of its logarithmic convergence-rate. We also
point out that MCTS in general has the worst-case time and space complexities
that depend on the state-set size which contradicts the original spirit of
MCTS. Unless heuristically used, UCT-based MCTS has yet to have theoretical
supports for its applicabilities.
