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I thank Deepak Agarwal for his discussion and for his interesting example. It is true that massive scale poses a challenge to Thompson sampling because it can be difficult to simulate from the required posterior distribution. The model in Deepak's example is a mixed effects logistic regression, with random effects for ad‐level covariates and fixed effects for interactions between user and ad creative characteristics. This is a true ‘big data’ problem, which raises issues orthogonal to those I sought to highlight in the article, but which are nonetheless critical for ad serving at LinkedIn and most other large Internet companies. Deepak proposes to treat the fixed effects and the variance of the random effects as known and to do approximate Thompson sampling based on the conditional distribution of the random effects. Given today's computing constraints, this is a reasonable approach. Another possibility would be to parallelize the posterior simulations using a technique like consensus Monte Carlo . Consensus Monte Carlo partitions the data across many worker machines. A full MCMC is run on each worker machine to learn a local posterior distribution for A and σ 2 . The local posterior distributions are combined to find the global
Applied Stochastic Models in Business and Industry – Wiley
Published: Jan 1, 2015
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