Algorithm 1 VIB based meta-reinforcement learning training algorithm.

1:Input:$\mathcal{D}$: training data set; ${\eta }_{\theta },{\eta }_{\phi },{\eta }_{\psi },{\eta }_{\omega }$ denote learning rate; ${\left\{{\mathcal{T}}_m\right\}}_{m=1,\dots ,M}\sim p(\mathcal{T})$: meta-training task set. 2:Output: policy network ${\pi }_{\theta }$ and latent space encoder $E_{\omega }$. 3:Setting parameter for the target network: $\psi \leftarrow \overline{\psi }$; the initial sample set for each task ${\mathcal{D}}^m$ 4:for epoch do 5:     for ${\mathcal{T}}_m$ do 6:          Initializing each trajectory: $e^{{\mathcal{T}}_m}=\left\{\right\}$ 7:          for $k=1,\cdots ,N$ do 8:             Latent space inference $z\sim E_{\omega }\left(\left.z\right|e^{{\mathcal{T}}_m}\right)$ 9:             The current policy ${\pi }_{\theta }\left(\left.a\right|s,z\right)$ interact with each task and obtain sample ${\mathcal{D}}^m$ 10:            Updating $e^{{\mathcal{T}}_m}={\left\{(s_j,a_j,s_j^{\prime },r_j)\right\}}_{j:1\dots K}\sim {\mathcal{D}}^m$ 11:         end for 12:    end for 13:    for step do 14:         for ${\mathcal{T}}_m$ do 15:           Sampling from the training data set: $e^{{\mathcal{T}}_m},d^m\sim {\mathcal{D}}^m$ 16:           Latent space inference: $z\sim E_{\omega }\left(\left.z\right|e^{{\mathcal{T}}_m}\right)$ 17:           Computing the action-state value function: ${\mathcal{J}}^m\left(Q\right)={\mathcal{J}}_{E_{\phi }}\left(d^m,z\right)$ 18:           Computing the state value function: ${\mathcal{J}}^m\left(V\right)={\mathcal{J}}_{E_{\psi }}\left(d^m,z\right)$ 19:           Computing the policy cost function: ${\mathcal{J}}^m\left(\pi \right)={\mathcal{J}}_{E_{\theta }}\left(d^m,z\right)$ 20:           Computing the latent space encoder cost function: ${\mathcal{J}}^m\left(E\right)={\mathcal{J}}_{E_{\omega }}\left(d^m,z\right)$ 21:         end for 22:         Updating the action-state value function network: ${\phi }_{t+1}\leftarrow {\phi }_t-{\eta }_{\phi }{\widehat{\nabla }}_{\phi }{\displaystyle {\displaystyle \sum }_m}{\mathcal{J}}^m\left(Q\right)$ 23:         Updating the state value function network: ${\psi }_{t+1}\leftarrow {\psi }_t-{\eta }_{\psi }{\widehat{\nabla }}_{\psi }{\displaystyle {\displaystyle \sum }_m}{\mathcal{J}}^m\left(V\right)$ 24:         Updating the policy network: ${\theta }_{t+1}\leftarrow {\theta }_t-{\eta }_{\theta }{\widehat{\nabla }}_{\theta }{\displaystyle {\displaystyle \sum }_m}{\mathcal{J}}^m\left(\pi \right)$ 25:         Updating the latent space encoder network: ${\omega }_{t+1}\leftarrow {\omega }_t-{\eta }_{\omega }{\widehat{\nabla }}_{\omega }{\displaystyle {\displaystyle \sum }_m}{\mathcal{J}}^m\left(E\right)$ 26:    end for 27:    Updating the target network $\psi \leftarrow \overline{\psi }$ 28:end for