They suggest a new algorithm and prove that it achieves logarithmic regret. Quality: Overall the results in the paper seem technically correct, but I had some concerns about the model/assumptions/results: - it is unclear to me how restrictive the parametric assumption that the expected log of the valuation is linear in the covariates. Although authors claim that predictor variables can be arbitrarily transformed, the task of designing the appropriate transformation, ie. "feature engineering", is a non-trivial task itself. Additionally it is unclear how realistic/flexible the logarithm/exponential relationship is, as it imposes that the valuations are exponentially far in relationship to the weighted covariate distances.