\begin{equation}
\begin{aligned}
L_k(x;\Theta_k)=&L_1(x;\Theta_k)-\sigma_2\sum_{j=1}^{k-1}s(x)\cdot|\log P(x)_{\mathrm{Agent}_k}-\log P(x)_{\mathrm{Agent}_j}| \\
=&[\log P(x)_{\mathrm{Prior}}-\log P(x)_{\mathrm{Agent}_k}+\sigma_1\cdot s(x)]^2\\
&-\sigma_2\sum_{j=1}^{k-1}s(x)\cdot|\log P(x)_{\mathrm{Agen}t_k}-\log P(x)_{\mathrm{Agent}_j}|
\end{aligned}
\end{equation}
