Fast Rates for Inverse Reinforcement Learning
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914567161905152 |
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| author | Schlaginhaufen, Andreas Kamgarpour, Maryam |
| author_facet | Schlaginhaufen, Andreas Kamgarpour, Maryam |
| contents | We establish novel structural and statistical results for entropy-regularized min-max inverse reinforcement learning (Min-Max-IRL) with linear reward classes in finite-horizon MDPs with Borel state and action spaces. On the structural side, we show that maximum likelihood estimation (MLE) and Min-Max-IRL are equivalent at the population level, and at the empirical level under deterministic dynamics. On the statistical side, exploiting pseudo-self-concordance of the Min-Max-IRL loss, we prove that both the trajectory-level KL divergence and the squared parameter error in the Hessian norm decay at the fast rate $\mathcal{O}(n^{-1})$, where $n$ is the number of expert trajectories. Our guarantees apply under misspecification and require no exploration assumptions. We further extend reward-identifiability results to general Borel spaces and derive novel results on the derivatives of the soft-optimal value function with respect to reward parameters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_14599 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fast Rates for Inverse Reinforcement Learning Schlaginhaufen, Andreas Kamgarpour, Maryam Machine Learning Artificial Intelligence We establish novel structural and statistical results for entropy-regularized min-max inverse reinforcement learning (Min-Max-IRL) with linear reward classes in finite-horizon MDPs with Borel state and action spaces. On the structural side, we show that maximum likelihood estimation (MLE) and Min-Max-IRL are equivalent at the population level, and at the empirical level under deterministic dynamics. On the statistical side, exploiting pseudo-self-concordance of the Min-Max-IRL loss, we prove that both the trajectory-level KL divergence and the squared parameter error in the Hessian norm decay at the fast rate $\mathcal{O}(n^{-1})$, where $n$ is the number of expert trajectories. Our guarantees apply under misspecification and require no exploration assumptions. We further extend reward-identifiability results to general Borel spaces and derive novel results on the derivatives of the soft-optimal value function with respect to reward parameters. |
| title | Fast Rates for Inverse Reinforcement Learning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.14599 |