Efficient Contextual Bandits in Non-stationary Worlds

Most contextual bandit algorithms minimize regret against the best fixed policy, a questionable benchmark for non-stationary environments that are ubiquitous in applications. In this work, we develop several efficient contextual bandit algorithms for non-stationary environments by equipping existing methods for i.i.d. problems with sophisticated statistical tests so as to dynamically adapt to a change in distribution.
We analyze various standard notions of regret suited to non-stationary environments for these algorithms, including interval regret, switching regret, and dynamic regret. When competing with the best policy at each time, one of our algorithms achieves regret \(O(\sqrt{ST})\) if there are \(T\) rounds with \(S\) stationary periods, or more generally \(O(\Delta^{1/3}T^{2/3})\) where \(\Delta\) is some non-stationarity measure. These results almost match the optimal guarantees achieved by an inefficient baseline that is a variant of the classic Exp4 algorithm. The dynamic regret result is also the first one for efficient and fully adversarial contextual bandit.
Furthermore, while the results above require tuning a parameter based on the unknown quantity \(S\) or \(\Delta\), we also develop a parameter free algorithm achieving regret \(\min\{S^{1/4}T^{3/4},\Delta^{1/5}T^{4/5}\}\). This improves and generalizes the best existing result \(\Delta^{0.18}T^{0.82}\) by Karnin and Anava (2016) which only holds for the two-armed bandit problem.