  We consider the multi armed bandit problem in non-stationary environments.
Based on the Bayesian method, we propose a variant of Thompson Sampling which
can be used in both rested and restless bandit scenarios. Applying discounting
to the parameters of prior distribution, we describe a way to systematically
reduce the effect of past observations. Further, we derive the exact expression
for the probability of picking sub-optimal arms. By increasing the exploitative
value of Bayes' samples, we also provide an optimistic version of the
algorithm. Extensive empirical analysis is conducted under various scenarios to
validate the utility of proposed algorithms. A comparison study with various
state-of-the-arm algorithms is also included.
