Abstract
We propose the first contextual bandit algorithm that is parameter-free, efficient, and optimal in terms of dynamic regret. Specifically, our algorithm achieves dynamic regret O(min{√ST, Δ^1/3T^2/3}) for a contextual bandit problem with T rounds, S switches and Δ total variation in data distributions. Importantly, our algorithm is adaptive and does not need to know S or Δ ahead of time, and can be implemented efficiently assuming access to an ERM oracle. Our results strictly improve the O(min {S^1/4T^3/4, Δ^1/5T^4/5}) bound of (Luo et al., 2018), and greatly generalize and improve the O(√ST) result of (Auer et al, 2018) that holds only for the two-armed bandit problem without contextual information. The key novelty of our algorithm is to introduce replay phases, in which the algorithm acts according to its previous decisions for a certain amount of time in order to detect non-stationarity while maintaining a good balance between exploration and exploitation.