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An Empirical Risk Minimization Approach for Offline Inverse RL and Dynamic Discrete Choice Model

Created by
  • Haebom

Author

Enoch H. Kang, Hema Yoganarasimhan, Lalit Jain

Outline

In this paper, we study the offline maximum entropy regularization inverse reinforcement learning (offline MaxEnt-IRL) problem in machine learning, namely the dynamic discrete choice (DDC) model. The goal is to recover the reward or Q* function that governs the agent's behavior from offline behavior data. We propose a global convergence-based gradient descent method to solve this problem without the restrictive assumption of linearly parameterized rewards. The novelty of this study lies in introducing an empirical risk minimization (ERM)-based IRL/DDC framework that does not require explicit state transition probability estimation in the Bellman equation. It is also compatible with nonparametric estimation techniques such as neural networks. Thus, the proposed method has the potential to be extended to high-dimensional, infinite state spaces. The key theoretical insight of this study is that the Bellman residual satisfies the Polyak-Lojasiewicz (PL) condition, which is weaker than the strong convexity but sufficient to guarantee fast global convergence. Through a series of synthetic experiments, we show that the proposed method consistently outperforms benchmark methods and state-of-the-art alternatives.

Takeaways, Limitations

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Takeaways:
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We present a global convergence-based gradient descent method that efficiently estimates DDC models without restrictive assumptions of linearly parameterized rewards.
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We introduce an ERM-based IRL/DDC framework that does not require explicit state transition probability estimation, thereby reducing computational cost and increasing scalability to high-dimensional problems.
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It suggests the possibility of extension to high-dimensional, infinite state spaces through compatibility with nonparametric estimation techniques.
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It provides fast global convergence guarantee by satisfying the PL condition of the Bellman residual.
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We verify superior performance compared to existing methods through synthetic experiments.
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Limitations:
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The performance of the proposed method is based on experimental results on synthetic data and requires validation on real data.
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The PL condition is a weaker condition than strong convexity, but it is not applicable to all problems. It may slow down convergence in certain problems.
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Further analysis of computational complexity and scalability in real-world applications is needed.
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