&\hspace{5mm}if \: \lambda \neq 0
      \      &\hspace{10mm} g_t \leftarrow g_t + \lambda
      \theta_{t-1}                            \      &\hspace{5mm}v_t
      \leftarrow   \alpha v_{t-1} + (1 - \alpha) g^2_t
      \hspace{8mm}
      \      &\hspace{5mm} \tilde{v_t} \leftarrow v_t
      \      &\hspace{5mm}if \: centered
      \      &\hspace{10mm} g^{ave}t \leftarrow g^{ave} \alpha
      + (1-\alpha) g_t            \      &\hspace{10mm} \tilde{v_t}
      \leftarrow \tilde{v_t} -  \big(g^{ave}{t} \big)^2        \
      &\hspace{5mm}if \: \mu > 0
      \      &\hspace{10mm} \textbf{b}_t\leftarrow \mu
      \textbf{b} +          g_t/ \big(\sqrt{\tilde{v_t}} +
      \epsilon \big)                                   \
      &\hspace{10mm} \theta_t \leftarrow \theta_{t-1} - \gamma
      \textbf{b}t                \      &\hspace{5mm} else
      \      &\hspace{10mm}\theta_t      \leftarrow   \theta -
      \gamma  g_t/ \big(\sqrt{\tilde{v_t}} + \epsilon \big)