Algorithm 1. Hybrid imitation learning framework.

Function HIL(D, $\mathsf{\rho }$) /* the demo dataset $\mathrm{D}=\left\{〈\left({\mathrm{s}}_{{\mathrm{k}}_1}^{\mathrm{E}},{\mathrm{a}}_{{\mathrm{k}}_1}^{\mathrm{E}}\right),\dots ,\left({\mathrm{s}}_{{\mathrm{k}}_l}^{\mathrm{E}},{\mathrm{a}}_{k_l}^{\mathrm{E}}\right)〉\right|\mathrm{k}=1,\dots ,\mathrm{n}\}$, the state recovery probability $\mathsf{\rho }$ */ Initialize the policy network ${\mathsf{\pi }}_{\mathsf{\theta }}$ and the dynamics network ${\mathrm{f}}_{\mathsf{\varphi }}$ ${\mathrm{f}}_{\mathsf{\varphi }}$ = Pretrain_Dynamics_Network(${\mathrm{f}}_{\mathsf{\varphi }},$  $\mathrm{D}$, $\mathrm{E}$) for e = 0,…, E epochs do   for I = 0,…,|D| do     Sample $\mathrm{d}=〈\left(s_1^E,a_1^E\right), \left(s_2^E,a_2^E\right),\dots , \left(s_l^E,a_l^E\right)〉$ from $\mathrm{D}$     ${\mathrm{L}}_{\mathrm{BC}},{\mathrm{d}}_{\mathrm{conv}}=$ Behavior_Cloning(${\mathsf{\pi }}_{\mathsf{\theta }}$, $\mathrm{d}$) ${\mathrm{L}}_{\mathrm{SC}}=$ State_Cloning(${\mathsf{\pi }}_{\mathsf{\theta }}$, ${\mathrm{f}}_{\mathsf{\varphi }},\mathrm{d}$, $\mathsf{\rho }$) ${\mathrm{L}}_{\mathrm{mix}}=$ Loss_Mixing(${\mathrm{L}}_{\mathrm{BC}}$, ${\mathrm{L}}_{\mathrm{SC}},{\mathrm{d}}_{\mathrm{c}onv}$)     Update the policy network parameters $\mathsf{\theta }$ by gradient descent          $\mathsf{\theta }\leftarrow \mathsf{\theta }-{\nabla }_{\mathsf{\theta }}{\mathrm{L}}_{\mathrm{mix}}$   end for end for return ${\mathsf{\pi }}_{\mathsf{\theta }}$