  In this paper we derive an efficient method for computing the indices
associated with an asymptotically optimal upper confidence bound algorithm
(MDP-UCB) of Burnetas and Katehakis (1997) that only requires solving a system
of two non-linear equations with two unknowns, irrespective of the cardinality
of the state space of the Markovian decision process (MDP). In addition, we
develop a similar acceleration for computing the indices for the
MDP-Deterministic Minimum Empirical Divergence (MDP-DMED) algorithm developed
in Cowan et al. (2019), based on ideas from Honda and Takemura (2011), that
involves solving a single equation of one variable. We provide experimental
results demonstrating the computational time savings and regret performance of
these algorithms. In these comparison we also consider the Optimistic Linear
Programming (OLP) algorithm (Tewari and Bartlett, 2008) and a method based on
Posterior sampling (MDP-PS).

Machine Learning;Artificial Intelligence;Machine Learning