  Motivated by a range of applications, we study in this paper the problem of
transfer learning for nonparametric contextual multi-armed bandits under the
covariate shift model, where we have data collected on source bandits before
the start of the target bandit learning. The minimax rate of convergence for
the cumulative regret is established and a novel transfer learning algorithm
that attains the minimax regret is proposed. The results quantify the
contribution of the data from the source domains for learning in the target
domain in the context of nonparametric contextual multi-armed bandits.
  In view of the general impossibility of adaptation to unknown smoothness, we
develop a data-driven algorithm that achieves near-optimal statistical
guarantees (up to a logarithmic factor) while automatically adapting to the
unknown parameters over a large collection of parameter spaces under an
additional self-similarity assumption. A simulation study is carried out to
illustrate the benefits of utilizing the data from the auxiliary source domains
for learning in the target domain.
