Title: On Abruptly-Changing and Slowly-Varying Multiarmed Bandit Problems,
Abstract: We study the non-stationary stochastic multiarmed bandit (MAB) problem and
propose two generic algorithms, namely, the limited memory deterministic
sequencing of exploration and exploitation (LM-DSEE) and the Sliding-Window
Upper Confidence Bound# (SW-UCB#). We rigorously analyze these algorithms in
abruptly-changing and slowly-varying environments and characterize their
performance. We show that the expected cumulative regret for these algorithms
under either of the environments is upper bounded by sublinear functions of
time, i.e., the time average of the regret asymptotically converges to zero. We
complement our analytic results with numerical illustrations.