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

2024-10-10

AI Summary

This work addresses the feasibility and stability of reward function transfer across environments in adversarial inverse reinforcement learning (AIRL) under high-dimensional or infinite state spaces. We propose a novel analytical framework grounded in random matrix theory. Our theoretical analysis reveals that reward transferability is both necessary and sufficient when the rank of the difference between the state transition matrix and the identity matrix satisfies a specific constraint—a condition that holds with high probability under standard random matrix assumptions. This marks the first application of random matrix theory to transfer analysis in inverse reinforcement learning. Furthermore, we identify policy optimization variance—not the AIRL framework itself—as the primary performance bottleneck. Leveraging this insight, we design a hybrid transfer framework combining PPO in the source environment and SAC in the target environment. Empirical evaluation on high-dimensional tasks demonstrates substantial improvements in reward recovery accuracy and robustness.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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 extbf{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.

Problem

• Adversarial Inverse Reinforcement Learning
• Reward Recovery
• Algorithm Stability

Innovation

• Adversarial Inverse Reinforcement Learning
• Reward Transfer
• Stochastic Matrix Theory