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Robust Reinforcement Learning with Dynamic Distortion Risk Measures

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  • Anthony Coache
  • Sebastian Jaimungal

Abstract

In a reinforcement learning (RL) setting, the agent's optimal strategy heavily depends on her risk preferences and the underlying model dynamics of the training environment. These two aspects influence the agent's ability to make well-informed and time-consistent decisions when facing testing environments. In this work, we devise a framework to solve robust risk-aware RL problems where we simultaneously account for environmental uncertainty and risk with a class of dynamic robust distortion risk measures. Robustness is introduced by considering all models within a Wasserstein ball around a reference model. We estimate such dynamic robust risk measures using neural networks by making use of strictly consistent scoring functions, derive policy gradient formulae using the quantile representation of distortion risk measures, and construct an actor-critic algorithm to solve this class of robust risk-aware RL problems. We demonstrate the performance of our algorithm on a portfolio allocation example.

Suggested Citation

  • Anthony Coache & Sebastian Jaimungal, 2024. "Robust Reinforcement Learning with Dynamic Distortion Risk Measures," Papers 2409.10096, arXiv.org.
  • Handle: RePEc:arx:papers:2409.10096
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    References listed on IDEAS

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    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    3. Saeed Marzban & Erick Delage & Jonathan Yu-Meng Li, 2023. "Deep reinforcement learning for option pricing and hedging under dynamic expectile risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 23(10), pages 1411-1430, October.
    4. Silvana M. Pesenti & Sebastian Jaimungal & Yuri F. Saporito & Rodrigo S. Targino, 2023. "Risk Budgeting Allocation for Dynamic Risk Measures," Papers 2305.11319, arXiv.org, revised Oct 2024.
    5. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    6. Carole Bernard & Silvana M. Pesenti & Steven Vanduffel, 2024. "Robust distortion risk measures," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 774-818, July.
    7. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    8. David Wu & Sebastian Jaimungal, 2023. "Robust Risk-Aware Option Hedging," Papers 2303.15216, arXiv.org, revised Dec 2023.
    9. David Wu & Sebastian Jaimungal, 2023. "Robust Risk-Aware Option Hedging," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(3), pages 153-174, May.
    10. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    11. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
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