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Generalization Capability for Imitation Learning

Yixiao Wang

TL;DR

This work addresses the generalization challenge in imitation learning by framing it within information theory and data distribution properties. It derives bounds on the generalization gap that depend on representation compression, encoder–dataset dependence, and the conditional entropy $H(Y|X)$, and analyzes both frozen and fine-tuned encoder regimes. Key insights show that reducing the mutual information $I(X;Z|Y)$ and $I(\phi;S)$ and increasing $H(Y|X)$ flatten the likelihood landscape and speed SGD’s convergence toward better minima, though training loss trade-offs and dataset design are crucial. Practically, the paper provides guidance on when to freeze pretrained encoders, how to diversify inputs and labels, and how to design data to improve generalization in robot policies, highlighting differences from domains like text-to-image generation.

Abstract

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.

Generalization Capability for Imitation Learning

TL;DR

This work addresses the generalization challenge in imitation learning by framing it within information theory and data distribution properties. It derives bounds on the generalization gap that depend on representation compression, encoder–dataset dependence, and the conditional entropy , and analyzes both frozen and fine-tuned encoder regimes. Key insights show that reducing the mutual information and and increasing flatten the likelihood landscape and speed SGD’s convergence toward better minima, though training loss trade-offs and dataset design are crucial. Practically, the paper provides guidance on when to freeze pretrained encoders, how to diversify inputs and labels, and how to design data to improve generalization in robot policies, highlighting differences from domains like text-to-image generation.

Abstract

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.

Paper Structure

This paper contains 13 sections, 6 theorems, 13 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Main Findings
  3. Actionable Guidelines
  4. Latent and Model Compressions Reduce Generalization Gap
  5. Definition of Generalization Gap
  6. Problem Statement
  7. Upper Bound of Generalization Gap
  8. Conclusion
  9. Data Distribution Properties Influence Generalization Capability
  10. Effect on Upper Bound of Generalization Gap
  11. Effect on Training Dynamics
  12. Conclusion
  13. Conclusion

Key Result

Theorem 1

kawaguchi2023does If $\phi_l^s(\cdot)$ is independent with the training dataset $s$, then for any $\delta>0$, with the probability at least $1-\delta$, the following holds: where $I(\cdot)$ is the mutual information,$G_1^l(0)=\Tilde{\mathcal{O}}(1)$, $G_3^l(0)=\Tilde{\mathcal{O}}(1)$, $\mathcal{G}_2^l=\Tilde{\mathcal{O}}(1)$ when $n\rightarrow \infty$, $l\in\{1,2,...,L\}$.

Figures (2)

  • Figure 1: Illustration on generalization gap in imitation learning. We would like to utilize finite number of data $\{(x_i,y_i)\}_{i=1}^n$ and generalize to the whole distribution $(X,Y)\sim \mathcal{P}$.
  • Figure 2: Common framework for imitation learning. (a) shows encoder all the information of $X$ together; (b) shows encoder large portion of $X$ such as image and lanuage through a large model, then together with intermediate representation $X$ with the rest of $X$, to generate the robot action $Y$.

Theorems & Definitions (6)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Lemma 1
  • Theorem 4
  • Theorem 5