# On Reward Transferability in Adversarial Inverse Reinforcement Learning: Insights from Random Matrix Theory

arXiv: https://arxiv.org/abs/2410.07643 · HTML: https://mlsanity.com/paper/2410.07643/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse reinforcement learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Placed in

- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)
- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Learning Robust Rewards with Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1710.11248/) (2017)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Model-Ensemble Trust-Region Policy Optimization](https://mlsanity.com/paper/1802.10592/) (2018)
- [Discriminator-Actor-Critic: Addressing Sample Inefficiency and Reward Bias in Adversarial Imitation Learning](https://mlsanity.com/paper/1809.02925/) (2018)
- [Imitation Learning via Off-Policy Distribution Matching](https://mlsanity.com/paper/1912.05032/) (2019)
- [Variational Information Maximisation for Intrinsically Motivated Reinforcement Learning](https://mlsanity.com/paper/1509.08731/) (2015)
- [Virtual-Taobao: Virtualizing Real-world Online Retail Environment for Reinforcement Learning](https://mlsanity.com/paper/1805.10000/) (2018)
- [State Alignment-based Imitation Learning](https://mlsanity.com/paper/1911.10947/) (2019)
- [f-IRL: Inverse Reinforcement Learning via State Marginal Matching](https://mlsanity.com/paper/2011.04709/) (2020)
- [Identifiability in inverse reinforcement learning](https://mlsanity.com/paper/2106.03498/) (2021)
- [Multi-Agent Imitation Learning for Driving Simulation](https://mlsanity.com/paper/1803.01044/) (2018)
- [Energy-Based Imitation Learning](https://mlsanity.com/paper/2004.09395/) (2020)
- [Adversarial Imitation via Variational Inverse Reinforcement Learning](https://mlsanity.com/paper/1809.06404/) (2018)
- [OPIRL: Sample Efficient Off-Policy Inverse Reinforcement Learning via Distribution Matching](https://mlsanity.com/paper/2109.04307/) (2021)
- [Receding Horizon Inverse Reinforcement Learning](https://mlsanity.com/paper/2206.04477/) (2022)
- [Off-Policy Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/2005.01138/) (2020)
- [BC-IRL: Learning Generalizable Reward Functions from Demonstrations](https://mlsanity.com/paper/2303.16194/) (2023)

## Abstract (arXiv)

In the context of inverse reinforcement learning (IRL) with a single expert, adversarial inverse reinforcement learning (AIRL) serves as a foundational approach to providing comprehensive and transferable task descriptions. However, AIRL faces practical performance challenges, primarily stemming from the framework's overly idealized decomposability condition, the unclear proof regarding the potential equilibrium in reward recovery, or questionable robustness in high-dimensional environments. This paper revisits AIRL in high-dimensional scenarios where the state space tends to infinity. Specifically, we first establish a necessary and sufficient condition for reward transferability by examining the rank of the matrix derived from subtracting the identity matrix from the transition matrix. Furthermore, leveraging random matrix theory, we analyze the spectral distribution of this matrix, demonstrating that our rank criterion holds with high probability even when the transition matrices are unobservable. This suggests that the limitations on transfer are not inherent to the AIRL framework itself, but are instead related to the training variance of the reinforcement learning algorithms employed within it. Based on this insight, we propose a hybrid framework that integrates on-policy proximal policy optimization in the source environment with off-policy soft actor-critic in the target environment, leading to significant improvements in reward transfer effectiveness.