# Deterministic and Discriminative Imitation (D2-Imitation): Revisiting Adversarial Imitation for Sample Efficiency

arXiv: https://arxiv.org/abs/2112.06054 · HTML: https://mlsanity.com/paper/2112.06054/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 11 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, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Discriminator-Actor-Critic: Addressing Sample Inefficiency and Reward Bias in Adversarial Imitation Learning](https://mlsanity.com/paper/1809.02925/) (2018)
- [A Divergence Minimization Perspective on Imitation Learning Methods](https://mlsanity.com/paper/1911.02256/) (2019)
- [Imitation Learning via Off-Policy Distribution Matching](https://mlsanity.com/paper/1912.05032/) (2019)
- [Imitation Learning as f-Divergence Minimization](https://mlsanity.com/paper/1905.12888/) (2019)
- [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)
- [On Convergence of Emphatic Temporal-Difference Learning](https://mlsanity.com/paper/1506.02582/) (2015)
- [Non-Adversarial Imitation Learning and its Connections to Adversarial Methods](https://mlsanity.com/paper/2008.03525/) (2020)
- [SoftDICE for Imitation Learning: Rethinking Off-policy Distribution Matching](https://mlsanity.com/paper/2106.03155/) (2021)

## Built on by (most cited first, 3 of 3)

- [Imitation Learning by State-Only Distribution Matching](https://mlsanity.com/paper/2202.04332/) (2022)
- [R2-Diff: Denoising by diffusion as a refinement of retrieved motion for image-based motion prediction](https://mlsanity.com/paper/2306.09483/) (2023)
- [Imitation Learning in the Deep Learning Era: A Novel Taxonomy and Recent Advances](https://mlsanity.com/paper/2511.03565/) (2025)

## Abstract (arXiv)

Sample efficiency is crucial for imitation learning methods to be applicable in real-world applications. Many studies improve sample efficiency by extending adversarial imitation to be off-policy regardless of the fact that these off-policy extensions could either change the original objective or involve complicated optimization. We revisit the foundation of adversarial imitation and propose an off-policy sample efficient approach that requires no adversarial training or min-max optimization. Our formulation capitalizes on two key insights: (1) the similarity between the Bellman equation and the stationary state-action distribution equation allows us to derive a novel temporal difference (TD) learning approach; and (2) the use of a deterministic policy simplifies the TD learning. Combined, these insights yield a practical algorithm, Deterministic and Discriminative Imitation (D2-Imitation), which operates by first partitioning samples into two replay buffers and then learning a deterministic policy via off-policy reinforcement learning. Our empirical results show that D2-Imitation is effective in achieving good sample efficiency, outperforming several off-policy extension approaches of adversarial imitation on many control tasks.