Factorization Bandits for Interactive Recommendation
نویسندگان
چکیده
(3) because ‖(xa,va)‖2 ≤ L and ηt only has a finite variance. For the first term on the right-hand side in Eq (2), if the regularization parameter λ1 is sufficiently large, the Hessian matrix of the loss function specified in the paper is positive definite at the optimizer based on the property of alternating least square (Uschmajew 2012). The estimation of Θ and va is thus locally q-linearly convergent to the optimizer. This indicates that for every 1 > 0, we have, ‖v̂a,t+1 − v a‖2 ≤ (q1 + 1)‖v̂a,t − v a‖2 (4) where 0 < q1 < 1. As a conclusion, we have for any δ > 0, with probability at least 1− δ,
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