Reviews: Linear Contextual Bandits with Knapsacks

My main comment is that the design of the proposed algorithm is not explained and justified well. In particular, the algorithm combines the ideas from both stochastic learning, such as the confidence intervals on \mu and W, and adversarial learning, the selection of \theta. At first, this raises eyebrows but I think that I understand. What I do not understand is why the learning of \theta is an adversarial problem. Can you elaborate on this?