  Popular Monte-Carlo tree search (MCTS) algorithms for online planning, such
as epsilon-greedy tree search and UCT, aim at rapidly identifying a reasonably
good action, but provide rather poor worst-case guarantees on performance
improvement over time. In contrast, a recently introduced MCTS algorithm BRUE
guarantees exponential-rate improvement over time, yet it is not geared towards
identifying reasonably good choices right at the go. We take a stand on the
individual strengths of these two classes of algorithms, and show how they can
be effectively connected. We then rationalize a principle of "selective tree
expansion", and suggest a concrete implementation of this principle within
MCTS. The resulting algorithm,s favorably compete with other MCTS algorithms
under short planning times, while preserving the attractive convergence
properties of BRUE.
