Algorithm 3: Distributed Online Model Evolving

input: Observation (${\mathit{z}}_{*},\mathit{y}({\mathit{z}}_{*})$), predictive distribution $\mathcal{N}(\mathit{\mu }({\mathit{z}}_{*}),{\mathit{\sigma }}^2({\mathit{z}}_{*}))$;  output: Updated hyper-parameters ${\mathit{\theta }}^{new}$;