Reviews: Nonparametric Contextual Bandits in Metric Spaces with Unknown Metric

The paper is clear, and makes efforts to highlight the behavior of the proposed algorithm (value of the regret bound for some specific settings, experiments measuring the impact of the metric). The comparison to other settings may still be enforced. In the experimental part, I would also appreciate the comparison to include some state of the art algorithms. What would be the empirical results of a gaussian process-based bandit? It would also be interesting to have results on datasets used by other contextual/similarity-based bandits (except that these datasets use a context in R d). Finally, it's surprising to have a context space of dimension 1. Extending the algorithm to R d setting seems strait-forward.