Versatile Offline Imitation from Observations and Examples via Regularized State-Occupancy Matching

TL;DR

This work introduces SMODICE, a regression-based offline imitation learning method grounded in state-occupancy matching. By leveraging $f$-divergence regularization and Fenchel duality, SMODICE derives a stable, uninterleaved optimization that first learns a discriminative reward over states, solves a dual value-function to obtain occupancy weights, and then performs weighted regression to recover the policy. It unifies imitation from observations, mismatched experts, and example-based RL under a single framework, providing closed-form solutions for tabular MDPs and strong empirical results on gridworlds and high-dimensional offline benchmarks. The method demonstrates superior robustness and performance across diverse offline data compositions, highlighting its practical potential in settings where expert actions or identical dynamics are unavailable.

Abstract

We propose State Matching Offline DIstribution Correction Estimation (SMODICE), a novel and versatile regression-based offline imitation learning (IL) algorithm derived via state-occupancy matching. We show that the SMODICE objective admits a simple optimization procedure through an application of Fenchel duality and an analytic solution in tabular MDPs. Without requiring access to expert actions, SMODICE can be effectively applied to three offline IL settings: (i) imitation from observations (IfO), (ii) IfO with dynamics or morphologically mismatched expert, and (iii) example-based reinforcement learning, which we show can be formulated as a state-occupancy matching problem. We extensively evaluate SMODICE on both gridworld environments as well as on high-dimensional offline benchmarks. Our results demonstrate that SMODICE is effective for all three problem settings and significantly outperforms prior state-of-art.

Figures (13)

• Figure 1: Diagram of SMODICE. First, a state-based discriminator is trained using the offline dataset $d^O$ and expert observations (resp. examples) $d^E$. Then, the discriminator is used to train the Lagrangian value function. Finally, the value function provides the importance weights for policy training, which outputs the learned policy $d^*$.
• Figure 2: Illustrations of tabular SMODICE for offline imitation learning from mismatched experts and examples.
• Figure 3: Illustrations of the evaluation environments.
• Figure 4: Offline imitation learning from observations results.
• Figure 5: Offline imitation learning from mismatched experts results.

Theorems & Definitions (17)

• Definition 1: $f$-divergence
• Definition 2: Fenchel conjugate
• Theorem 1
• Theorem 2
• Theorem 3
• Lemma 1
• proof
• Lemma 2
• proof
• proof