  The upper confidence reinforcement learning (UCRL2) algorithm introduced in
(Jaksch et al., 2010) is a popular method to perform regret minimization in
unknown discrete Markov Decision Processes under the average-reward criterion.
Despite its nice and generic theoretical regret guarantees, this algorithm and
its variants have remained until now mostly theoretical as numerical
experiments in simple environments exhibit long burn-in phases before the
learning takes place. In pursuit of practical efficiency, we present UCRL3,
following the lines of UCRL2, but with two key modifications: First, it uses
state-of-the-art time-uniform concentration inequalities to compute confidence
sets on the reward and (component-wise) transition distributions for each
state-action pair. Furthermore, to tighten exploration, it uses an adaptive
computation of the support of each transition distribution, which in turn
enables us to revisit the extended value iteration procedure of UCRL2 to
optimize over distributions with reduced support by disregarding low
probability transitions, while still ensuring near-optimism. We demonstrate,
through numerical experiments in standard environments, that reducing
exploration this way yields a substantial numerical improvement compared to
UCRL2 and its variants. On the theoretical side, these key modifications enable
us to derive a regret bound for UCRL3 improving on UCRL2, that for the first
time makes appear notions of local diameter and local effective support, thanks
to variance-aware concentration bounds.
