Liquid Networks with Mixture Density Heads for Efficient Imitation Learning

While diffusion-based policies have impressive performance and expressivity, their long offline training slows down the data collection and policy deployment loop. We introduce Closed-Form Diffusion Policies, a class of training-free diffusion-based policies for imitation learning using the closed-form score derived from the demonstration dataset. We deploy CFDP with real-time inference with a mobile CPU in hardware experiments, showing it can successfully perform imitation directly from the dataset in milliseconds and with faster inference than neural diffusion policies. In experiments on imitation learning benchmarks, we show that CFDP is competitive against neural baselines that require hours of training, providing a favorable tradeoff between training time and performance. Finally, we show how closed-form diffusion policies act as a composable primitive that enables data-driven inference-time editing of pre-trained neural diffusion policies, including policy guidance and novel demonstration augmentation.

Semi-supervised imitation learning (SSIL) consists in learning a policy from a small dataset of action-labeled trajectories and a much larger dataset of action-free trajectories. Some SSIL methods learn an inverse dynamics model (IDM) to predict the action from the current state and the next state. An IDM can act as a policy when paired with a video model (VM-IDM) or as a label generator to perform behavior cloning on action-free data (IDM labeling). In this work, we first show that VM-IDM and IDM labeling learn the same policy in a limit case, which we call the IDM-based policy. We then argue that the previously observed advantage of IDM-based policies over behavior cloning is due to the superior sample efficiency of IDM learning, which we attribute to two causes: (i) the ground-truth IDM tends to be contained in a lower complexity hypothesis class relative to the expert policy, and (ii) the ground-truth IDM is often less stochastic than the expert policy. We argue these claims based on insights from statistical learning theory and novel experiments, including a study of IDM-based policies using recent architectures for unified video-action prediction (UVA). Motivated by these insights, we finally propose an improved version of the existing LAPO algorithm for latent action policy learning. We experiment on the Procgen, Push-T and LIBERO benchmarks.

Parametric imitation learning via behavior cloning can suffer from poor generalization to out-of-distribution states due to compounding errors during deployment. We show that reusing the training data during inference via a semi-parametric retrieval-based imitation learning approach can alleviate this challenge. We present Difference-Aware Retrieval Policies for Imitation Learning (DARP), a semi-parametric retrieval-based imitation learning approach that addresses this limitation by reparameterizing the imitation learning problem in terms of local neighborhood structure rather than direct state-to-action mappings. Instead of learning a global policy, DARP trains a model to predict actions based on $k$-nearest neighbors from expert demonstrations, their corresponding actions, and the relative distance vectors between neighbor states and query states. DARP requires no additional assumptions beyond those made for standard behavior cloning -- it does not require additional data collection, online expert feedback, or task-specific knowledge. We demonstrate consistent performance improvements of 15-46% over standard behavior cloning across diverse domains, including continuous control and robotic manipulation, and across different representations, including high-dimensional visual features. Code and demos are available at https://weirdlabuw.github.io/darp-site/.