  We consider online planning in Markov decision processes (MDPs). In online
planning, the agent focuses on its current state only, deliberates about the
set of possible policies from that state onwards and, when interrupted, uses
the outcome of that exploratory deliberation to choose what action to perform
next. The performance of algorithms for online planning is assessed in terms of
simple regret, which is the agent's expected performance loss when the chosen
action, rather than an optimal one, is followed.
  To date, state-of-the-art algorithms for online planning in general MDPs are
either best effort, or guarantee only polynomial-rate reduction of simple
regret over time. Here we introduce a new Monte-Carlo tree search algorithm,
BRUE, that guarantees exponential-rate reduction of simple regret and error
probability. This algorithm is based on a simple yet non-standard state-space
sampling scheme, MCTS2e, in which different parts of each sample are dedicated
to different exploratory objectives. Our empirical evaluation shows that BRUE
not only provides superior performance guarantees, but is also very effective
in practice and favorably compares to state-of-the-art. We then extend BRUE
with a variant of "learning by forgetting." The resulting set of algorithms,
BRUE(alpha), generalizes BRUE, improves the exponential factor in the upper
bound on its reduction rate, and exhibits even more attractive empirical
performance.
