Policy Newton methods for Distortion Riskmetrics
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909731046555648 |
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| author | Pachal, Soumen Maniyar, Mizhaan Prajit A, Prashanth L. |
| author_facet | Pachal, Soumen Maniyar, Mizhaan Prajit A, Prashanth L. |
| contents | We consider the problem of risk-sensitive control in a reinforcement learning (RL) framework. In particular, we aim to find a risk-optimal policy by maximizing the distortion riskmetric (DRM) of the discounted reward in a finite horizon Markov decision process (MDP). DRMs are a rich class of risk measures that include several well-known risk measures as special cases. We derive a policy Hessian theorem for the DRM objective using the likelihood ratio method. Using this result, we propose a natural DRM Hessian estimator from sample trajectories of the underlying MDP. Next, we present a cubic-regularized policy Newton algorithm for solving this problem in an on-policy RL setting using estimates of the DRM gradient and Hessian. Our proposed algorithm is shown to converge to an $ε$-second-order stationary point ($ε$-SOSP) of the DRM objective, and this guarantee ensures the escaping of saddle points. The sample complexity of our algorithms to find an $ ε$-SOSP is $\mathcal{O}(ε^{-3.5})$. Our experiments validate the theoretical findings. To the best of our knowledge, our is the first work to present convergence to an $ε$-SOSP of a risk-sensitive objective, while existing works in the literature have either shown convergence to a first-order stationary point of a risk-sensitive objective, or a SOSP of a risk-neutral one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07249 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Policy Newton methods for Distortion Riskmetrics Pachal, Soumen Maniyar, Mizhaan Prajit A, Prashanth L. Machine Learning We consider the problem of risk-sensitive control in a reinforcement learning (RL) framework. In particular, we aim to find a risk-optimal policy by maximizing the distortion riskmetric (DRM) of the discounted reward in a finite horizon Markov decision process (MDP). DRMs are a rich class of risk measures that include several well-known risk measures as special cases. We derive a policy Hessian theorem for the DRM objective using the likelihood ratio method. Using this result, we propose a natural DRM Hessian estimator from sample trajectories of the underlying MDP. Next, we present a cubic-regularized policy Newton algorithm for solving this problem in an on-policy RL setting using estimates of the DRM gradient and Hessian. Our proposed algorithm is shown to converge to an $ε$-second-order stationary point ($ε$-SOSP) of the DRM objective, and this guarantee ensures the escaping of saddle points. The sample complexity of our algorithms to find an $ ε$-SOSP is $\mathcal{O}(ε^{-3.5})$. Our experiments validate the theoretical findings. To the best of our knowledge, our is the first work to present convergence to an $ε$-SOSP of a risk-sensitive objective, while existing works in the literature have either shown convergence to a first-order stationary point of a risk-sensitive objective, or a SOSP of a risk-neutral one. |
| title | Policy Newton methods for Distortion Riskmetrics |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.07249 |