从信息论角度揭示模仿学习泛化能力的瓶颈与优化方向

Imitation learning holds the promise of equipping robots with versatile skills by learning from expert demonstrations. However, policies trained on finite datasets often struggle to generalize beyond the training distribution. In this work, we present a unified perspective on the generalization capability of imitation learning, grounded in both information theorey and data distribution property. We first show that the generalization gap can be upper bounded by (i) the conditional information bottleneck on intermediate representations and (ii) the mutual information between the model parameters and the training dataset. This characterization provides theoretical guidance for designing effective training strategies in imitation learning, particularly in determining whether to freeze, fine-tune, or train large pretrained encoders (e.g., vision-language models or vision foundation models) from scratch to achieve better generalization. Furthermore, we demonstrate that high conditional entropy from input to output induces a flatter likelihood landscape, thereby reducing the upper bound on the generalization gap. In addition, it shortens the stochastic gradient descent (SGD) escape time from sharp local minima, which may increase the likelihood of reaching global optima under fixed optimization budgets. These insights explain why imitation learning often exhibits limited generalization and underscore the importance of not only scaling the diversity of input data but also enriching the variability of output labels conditioned on the same input.