How to Mitigate the Distribution Shift Problem in Robotics Control: A Robust and Adaptive Approach Based on Offline to Online Imitation Learning

Imitation learning (IL) has achieved remarkable success in complex decision-making tasks. However, its performance is highly sensitive to distribution shifts, which can pose significant safety risks. We propose a distributionally robust and safe IL framework that explicitly addresses both policy-induced and uncertainty-induced distribution shifts. Our approach develops a unified framework leveraging Taylor Series Imitation Learning (TaSIL) to mitigate policy-induced shifts and distributionally robust adaptive control to handle uncertainty-induced shifts. This architecture enables the formulation of an IL problem that optimizes performance under distributional uncertainty while systematically accounting for safety constraints. We demonstrate the effectiveness of the proposed approach on an unmanned aerial vehicle (UAV) case study where the UAV performs a task in an uncertain environment while avoiding unsafe regions.

In robotics, a common challenge in imitation learning is the mismatch between training and deployment conditions, caused, for example, by environmental changes or imperfect observation and control. When a robot follows a nominal trajectory under such mismatch, it may become stuck and fail to complete the task. This calls for adaptive online exploration strategies that remain grounded in demonstrations. To this end, we propose an adaptive ergodic imitation approach that constructs a target distribution from the geometry of the retrieved demonstrations and uses it to generate trajectories that adaptively interpolate between tracking and exploration. Our method extends ergodic control beyond its traditional role in area-coverage and search by incorporating demonstrations into a retrieval-based receding-horizon framework for adaptive imitation.

Visuomotor policies trained via behavior cloning are vulnerable to covariate shift, where small deviations from expert trajectories can compound into failure. Common strategies to mitigate this issue involve expanding the training distribution through human-in-the-loop corrections or synthetic data augmentation. However, these approaches are often labor-intensive, rely on strong task assumptions, or compromise the quality of imitation. We introduce Latent Policy Barrier, a framework for robust visuomotor policy learning. Inspired by Control Barrier Functions, LPB treats the latent embeddings of expert demonstrations as an implicit barrier separating safe, in-distribution states from unsafe, out-of-distribution (OOD) ones. Our approach decouples the role of precise expert imitation and OOD recovery into two separate modules: a base diffusion policy solely on expert data, and a dynamics model trained on both expert and suboptimal policy rollout data. At inference time, the dynamics model predicts future latent states and optimizes them to stay within the expert distribution. Both simulated and real-world experiments show that LPB improves both policy robustness and data efficiency, enabling reliable manipulation from limited expert data and without additional human correction or annotation.