# Probability Density Estimation Based Imitation Learning

arXiv: https://arxiv.org/abs/2112.06746 · HTML: https://mlsanity.com/paper/2112.06746/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 13 Dec 2021.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 10 of 10)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [Primal Wasserstein Imitation Learning](https://mlsanity.com/paper/2006.04678/) (2020)
- [Random Expert Distillation: Imitation Learning via Expert Policy Support Estimation](https://mlsanity.com/paper/1905.06750/) (2019)
- [Watch, Try, Learn: Meta-Learning from Demonstrations and Reward](https://mlsanity.com/paper/1906.03352/) (2019)

## Abstract (arXiv)

Imitation Learning (IL) is an effective learning paradigm exploiting the interactions between agents and environments. It does not require explicit reward signals and instead tries to recover desired policies using expert demonstrations. In general, IL methods can be categorized into Behavioral Cloning (BC) and Inverse Reinforcement Learning (IRL). In this work, a novel reward function based on probability density estimation is proposed for IRL, which can significantly reduce the complexity of existing IRL methods. Furthermore, we prove that the theoretically optimal policy derived from our reward function is identical to the expert policy as long as it is deterministic. Consequently, an IRL problem can be gracefully transformed into a probability density estimation problem. Based on the proposed reward function, we present a "watch-try-learn" style framework named Probability Density Estimation based Imitation Learning (PDEIL), which can work in both discrete and continuous action spaces. Finally, comprehensive experiments in the Gym environment show that PDEIL is much more efficient than existing algorithms in recovering rewards close to the ground truth.