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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper studies the multi-armed bandit problem where they have a set of relevant features; and the expected reward of an action is a Lipschitz continuous of relevant features. This is also a feature selection problem where you have a set of features but only r of them are relevant (the target function only depends on r of these features): here each arm has only one relevant feature, meaning the function representing the arm payoff depending on only one feature and we do not know which one. They propose an algorithm and get the bound for such adaptive case; but their regret is higher than what you would get if someone tells you the relevant type. Q2: Please summarize your review in 1-2 sentences This paper makes a small step towards understanding the problem of having a subset of features being relevant for a given arm which itself is certainly an interesting problem: they study the bandit problem only for one relevant feature per arm and did not give the optimal rate. Potentially, they could go with all arbitrary number of relevant features and figure out the optimal regret.