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Imitation Learning as $f$-Divergence Minimization

Liyiming Ke, Sanjiban Choudhury, Matt Barnes, Wen Sun, Gilwoo Lee, Siddhartha Srinivasa

TL;DR

The paper reframes imitation learning with multi-modal demonstrations as f-divergence minimization between the learner and expert distributions, introducing a unifying variational framework (f-VIM) that recovers Behavior Cloning, GAIL, and DAgger as special cases. It contrasts mode-covering divergences (KL, JS) with the mode-seeking reverse KL (I-projection), showing that RKL tends to collapse to a single demonstrator mode and can improve safety and reliability in multi-modal tasks. By deriving tractable state-action-based surrogates and employing variational estimators, the authors enable scalable imitation across divergences and provide interactive variants to further optimize performance. The framework offers theoretical insights and practical algorithms for robust multi-modal imitation, with potential broad impact on robotics and sequential decision-making where demonstrations exhibit variability. Overall, this work unifies IL methods under f-divergence minimization and demonstrates the practical advantages of using reverse KL to handle multi-modal expert behavior.

Abstract

We address the problem of imitation learning with multi-modal demonstrations. Instead of attempting to learn all modes, we argue that in many tasks it is sufficient to imitate any one of them. We show that the state-of-the-art methods such as GAIL and behavior cloning, due to their choice of loss function, often incorrectly interpolate between such modes. Our key insight is to minimize the right divergence between the learner and the expert state-action distributions, namely the reverse KL divergence or I-projection. We propose a general imitation learning framework for estimating and minimizing any f-Divergence. By plugging in different divergences, we are able to recover existing algorithms such as Behavior Cloning (Kullback-Leibler), GAIL (Jensen Shannon) and Dagger (Total Variation). Empirical results show that our approximate I-projection technique is able to imitate multi-modal behaviors more reliably than GAIL and behavior cloning.

Imitation Learning as $f$-Divergence Minimization

TL;DR

The paper reframes imitation learning with multi-modal demonstrations as f-divergence minimization between the learner and expert distributions, introducing a unifying variational framework (f-VIM) that recovers Behavior Cloning, GAIL, and DAgger as special cases. It contrasts mode-covering divergences (KL, JS) with the mode-seeking reverse KL (I-projection), showing that RKL tends to collapse to a single demonstrator mode and can improve safety and reliability in multi-modal tasks. By deriving tractable state-action-based surrogates and employing variational estimators, the authors enable scalable imitation across divergences and provide interactive variants to further optimize performance. The framework offers theoretical insights and practical algorithms for robust multi-modal imitation, with potential broad impact on robotics and sequential decision-making where demonstrations exhibit variability. Overall, this work unifies IL methods under f-divergence minimization and demonstrates the practical advantages of using reverse KL to handle multi-modal expert behavior.

Abstract

We address the problem of imitation learning with multi-modal demonstrations. Instead of attempting to learn all modes, we argue that in many tasks it is sufficient to imitate any one of them. We show that the state-of-the-art methods such as GAIL and behavior cloning, due to their choice of loss function, often incorrectly interpolate between such modes. Our key insight is to minimize the right divergence between the learner and the expert state-action distributions, namely the reverse KL divergence or I-projection. We propose a general imitation learning framework for estimating and minimizing any f-Divergence. By plugging in different divergences, we are able to recover existing algorithms such as Behavior Cloning (Kullback-Leibler), GAIL (Jensen Shannon) and Dagger (Total Variation). Empirical results show that our approximate I-projection technique is able to imitate multi-modal behaviors more reliably than GAIL and behavior cloning.

Paper Structure

This paper contains 8 sections, 1 theorem, 6 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Preliminaries
  5. The f-divergence family
  6. Imitation learning as f-divergence minimization
  7. Framework for Divergence Minimization
  8. Variational approximation of divergence

Key Result

theorem thmcountertheorem

Given two policies $\pi$ and $\pi^*$, the f-divergence between trajectory distribution is lower bounded by f-divergence between average state-action distribution.

Figures (1)

  • Figure 1: Behavior cloning fails with multi-modal demonstrations. Experts go left or right around obstacle. Learner interpolates between modes and crashes into obstacle.

Theorems & Definitions (1)

  • theorem thmcountertheorem: Proof in Appendix \ref{['sec:state_action_distribution']}