Material to “ Online Clustering of Bandits ”
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چکیده
This supplementary material contains all proofs and technical details omitted from the main text, along with ancillary comments, discussion about related work, and extra experimental results. 1. Proof of Theorem 1 The following sequence of lemmas are of preliminary importance. The first one needs extra variance conditions on the process X generating the context vectors. We find it convenient to introduce the node counterpart to TCBj,t−1(x), and the cluster counterpart to T̃CBi,t−1. Given round t, node i ∈ V , and cluster index j ∈ {1, . . . ,mt}, we let TCBi,t−1(x) = √ x⊤M−1 i,t−1x ( σ √ 2 log |Mi,t−1| δ/2 + 1 ) T̃CBj,t−1 = σ √ 2d log t+ 2 log(2/δ) + 1 √ 1 +Aλ(T̄j,t−1, δ/(2m+1d)) ,
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تاریخ انتشار 2014