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(√ST) if there are T rounds with S stationary periods, or more generally O(Delta1/3T2/3) 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 minS1/4T3/4, Delta1/5T4/5. This improves and generalizes the best existing result Delta0.18T0.82 by Karnin and Anava (2016) which only holds for the two-armed bandit problem.