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Derive equation for regularized logistic regression with batch updates

I am trying to understand this paper by Chapelle and Li "An Empirical Evaluation of Thompson Sampling" (2011). In particular, I am failing to derive the equations in algorithm 3 (page 6). The first eq …
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Derive equation for regularized logistic regression with batch updates

I found the solution (with the help of a friend: cudos!). The posterior is $$\begin{align*} -\log p(\boldsymbol{w}|\boldsymbol{x}) &= -\log p(\boldsymbol{x}|\boldsymbol{w}) - \log p(\boldsymbol{w}) + …
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