                       \\
            &\hspace{10mm} g_t \leftarrow g_t + \lambda  \theta_{t-1}                            \\
            &\hspace{5mm} v_t      \leftarrow v_{t-1} \rho + g^2_t (1 - \rho)                    \\
            &\hspace{5mm}\Delta x_t    \leftarrow   \frac{\sqrt{u_{t-1} +
                \epsilon }}{ \sqrt{v_t + \epsilon}  }g_t \hspace{21mm}                           \\
            &\hspace{5mm} u_t  \leftarrow   u_{t-1}  \rho +
                 \Delta x^2_t  (1 - \rho)                                                        \\
            &\hspace{5mm}\theta_t      \leftarrow   \theta_{t-1} - \gamma  \Delta x_t            \\
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
            &\bf{return} \:  \theta_t                                                     \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
       \end{aligned}

    For further details regarding the algorithm we refer to `ADADELTA: An Adaptive Learning Rate Method`_.
    aD