In this work, we explore the idea of expert intervention delays in human-supervised robotic systems for imitation learning system. Previous works in imitation learning have primarily examined the impact of suboptimal experts, where the expert policy makes mistakes, but assumed expert interventions occur immediately after errors are made. Although delayed expert intervention can be viewed as a form of noise that might improve policy robustness, our results show that learning from delayed expert interventions is overall less effective than learning from non-delayed expert interventions; delayed expert interventions are less effective at demonstrating error avoidance behaviors. To address this, we propose Learning from Delayed Intervention (LfDI), which learns a cost function based on where and when the expert intervenes, combined with limited information about the extent of intervention delays provided by the expert. This cost function is then used to infer additional supervision for states without expert data, guiding the policy to avoid states that would likely trigger interventions. We evaluate our method, Learning from Delayed Intervention (LfDI), on simulated environments and show that it outperforms other methods that do not account for intervention delays.

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