  This brief paper presents simple simulation-based algorithms for obtaining an
approximately optimal policy in a given finite set in large finite constrained
Markov decision processes. The algorithms are adapted from playing strategies
for "sleeping experts and bandits" problem and their computational complexities
are independent of state and action space sizes if the given policy set is
relatively small. We establish convergence of their expected performances to
the value of an optimal policy and convergence rates, and also almost-sure
convergence to an optimal policy with an exponential rate for the algorithm
adapted within the context of sleeping experts.
