Problem: 

(1) Since expert actions are restricted by the interface, the IRL reward should be decoupled from the expert action, defined for state-state transitions rather than state-action. 

(2) Since demonstrations cover only part of the state space, a learning agent must identify which explored states have reliable reward estimates. 

(3) For the novel states encountered during exploration, the agent requires a generalizable reward signal.

Solution: We propose the LfCD with Goal-proximity Reward InterPolation(LfCD-GRIP) framework:

(1) Goal-proximity reward depends on state only,  measuring progress toward the goal.

(2) Confidence Estimator identifies expert-like observations where goal proximity reward is valid. 

(3) Proximity Interpolation Mechanism propagates task progress to the novel states.

 Through extensive experiments, including real-world validation on a WidowX robotic arm, we show that our approach outperforms baseline methods in final task performance.

Figure 1: Task completion time under different settings. The top row shows results with unconstrained experts, while the bottom row shows results with constrained experts. LfCD-GRIP performs competitively when action spaces are restricted, and significantly outperforms other baselines once the agent has access to the full action space.