    \begin{equation}
    \begin{split}
    &D_{\textnormal{KL}}\bigg(\underset{\mathbb{S}\sim Q^{m}}{\mathbb{E}}dis_{\rho_{\mathbb{S}}}^{MV}(\mathbb{S}_{\mathcal{X}},\mathbb{T}_{\mathcal{X}}),\underset{\mathbb{S}\sim Q^{m}}{\mathbb{E}}dis_{\rho_{\mathbb{S}}}^{MV}(Q_{\mathcal{X}},P_{\mathcal{X}})\bigg)\\
    \leq &\frac{1}{m}\Bigg[\underset{\mathbb{S}\sim Q^{m}}{\mathbb{E}}\,\underset{v\sim \rho_{\mathbb{S}}}{\mathbb{E}}2D_{\textnormal{KL}}(\mathcal{Q}_{v,\mathbb{S}}\Vert\mathcal{P}_{v}) + \underset{\mathbb{S}\sim Q^{m}}{\mathbb{E}}2D_{\textnormal{KL}}(\rho_{\mathbb{S}}\Vert\pi) + \ln{\frac{2\sqrt{m}}{\delta}}\Bigg].
        \end{split}
    \end{equation}
