error logic in LinUCB

[liangqq6]

In paper "A Contextual-Bandit Approach to Personalized News Article Recommendation", algorithm LinUCB does not consider the differences between users.
Users' information are only contained in contextFeatureVector, which is referred to "x_t,a" in Algorithm 1. Also, variables "A", "b", "theta" varied from arms(articles) rather than users.
Therefore, I wonder if there are mistakes in class LinUCBUserStruct in your code. I do not think it needs structure for each user and the implementation of "A", "b", "theta" may be wrong.
Could you help me figure out this confusion, thanks!

[qingyun-wu]

Hi, Thank you for your email. There are indeed some differences between our studied setting and the setting in the original LinUCB paper <http://rob.schapire.net/papers/www10.pdf> need to clarify: The original paper of LinUCB indeed does not consider the difference between users and the bandit models are built on the arm/item side (i.e, A, b, \theta are attached to each arm). But in our work, we are working on a different setting where we introduce the concept of users (mainly because we want to apply it to personalized recommendation tasks and further study the effect of collaboration among users) and bandit models are built on the user side (i.e, A, b, \theta are attached to each user), which is why we have a LinUCBUserStruct class. In our setting, contextFeatureVector "x_t,a" are all about arms/items a at time t. In other words, which setting to take totally depends on how you want to model the problem. More specifically, if you need to work on the setting in the original LinUCB paper, you can change the LinUCBUserStruct into LinUCBArmStruct such that variables "A", "b", "theta" varied from each arms(articles). Please feel free to let us know if my explanation is not clear or if you have more comments. Thank you again for your email.

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On Tue, Nov 13, 2018 at 2:25 AM liangqq6 ***@***.***> wrote: In paper , algorithm LinUCB does not consider the difference of each user. Users' information are only contained in contextFeatureVector, which is referred to "x_t,a" in Algorithm 1. Also, variables "A", "b", "theta" varied from each arms(articles) rather than users. Therefore, I wonder if there are mistakes in class LinUCBUserStruct in your code. I do not think it needs structure for each user and the implementation of "A", "b", "theta" may be wrong. Could you help me figure out this confusion, thanks! — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#3>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AIgdNMtI0LDmYf6FH9DlVLEs-Y-T2yq9ks5uunPYgaJpZM4YbD0w> .

-- Qingyun Wu Ph.D Candidate Department of Computer Science University of Virginia Email: qw2ky@virginia.edu