# Learning from Sparse Demonstrations

arXiv: https://arxiv.org/abs/2008.02159 · HTML: https://mlsanity.com/paper/2008.02159/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2020.

## Built on by (most cited first, 9 of 9)

- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [OpenVR: Teleoperation for Manipulation](https://mlsanity.com/paper/2305.09765/) (2023)
- [Online Control-Informed Learning](https://mlsanity.com/paper/2410.03924/) (2024)
- [Language-Model-Assisted Bi-Level Programming for Reward Learning from Internet Videos](https://mlsanity.com/paper/2410.09286/) (2024)
- [Pontryagin Optimal Control via Neural Networks](https://mlsanity.com/paper/2212.14566/) (2022)
- [A Differential Dynamic Programming Framework for Inverse Reinforcement Learning](https://mlsanity.com/paper/2407.19902/) (2024)
- [Distributed Differentiable Dynamic Game for Multi-robot Coordination](https://mlsanity.com/paper/2207.08892/) (2022)
- [Learning Time-Invariant Reward Functions through Model-Based Inverse Reinforcement Learning](https://mlsanity.com/paper/2107.03186/) (2021)
- [Adaptive Policy Learning to Additional Tasks](https://mlsanity.com/paper/2305.15193/) (2023)

## Abstract (arXiv)

This paper develops the method of Continuous Pontryagin Differentiable Programming (Continuous PDP), which enables a robot to learn an objective function from a few sparsely demonstrated keyframes. The keyframes, labeled with some time stamps, are the desired task-space outputs, which a robot is expected to follow sequentially. The time stamps of the keyframes can be different from the time of the robot's actual execution. The method jointly finds an objective function and a time-warping function such that the robot's resulting trajectory sequentially follows the keyframes with minimal discrepancy loss. The Continuous PDP minimizes the discrepancy loss using projected gradient descent, by efficiently solving the gradient of the robot trajectory with respect to the unknown parameters. The method is first evaluated on a simulated robot arm and then applied to a 6-DoF quadrotor to learn an objective function for motion planning in unmodeled environments. The results show the efficiency of the method, its ability to handle time misalignment between keyframes and robot execution, and the generalization of objective learning into unseen motion conditions.