  We consider the model selection task in the stochastic contextual bandit
setting. Suppose we are given a collection of base contextual bandit
algorithms. We provide a master algorithm that combines them and achieves the
same performance, up to constants, as the best base algorithm would, if it had
been run on its own. Our approach only requires that each algorithm satisfy a
high probability regret bound.
  Our procedure is very simple and essentially does the following: for a well
chosen sequence of probabilities $(p_{t})_{t\geq 1}$, at each round $t$, it
either chooses at random which candidate to follow (with probability $p_{t}$)
or compares, at the same internal sample size for each candidate, the
cumulative reward of each, and selects the one that wins the comparison (with
probability $1-p_{t}$).
  To the best of our knowledge, our proposal is the first one to be
rate-adaptive for a collection of general black-box contextual bandit
algorithms: it achieves the same regret rate as the best candidate.
  We demonstrate the effectiveness of our method with simulation studies.
