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Algorithmic aspects of mean–variance optimization in Markov decision processes

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  • Mannor, Shie
  • Tsitsiklis, John N.

Abstract

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for others. We finally offer pseudopolynomial exact and approximation algorithms.

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  • Mannor, Shie & Tsitsiklis, John N., 2013. "Algorithmic aspects of mean–variance optimization in Markov decision processes," European Journal of Operational Research, Elsevier, vol. 231(3), pages 645-653.
    • Handle: RePEc:eee:ejores:v:231:y:2013:i:3:p:645-653
    DOI: 10.1016/j.ejor.2013.06.019
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Haoran Wang & Xun Yu Zhou, 2020. "Continuous‐time mean–variance portfolio selection: A reinforcement learning framework," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1273-1308, October.
    2. Thomas Spooner & Rahul Savani, 2020. "A Natural Actor-Critic Algorithm with Downside Risk Constraints," Papers 2007.04203, arXiv.org.
    3. Jingnan Fan & Andrzej Ruszczynski, 2014. "Process-Based Risk Measures and Risk-Averse Control of Discrete-Time Systems," Papers 1411.2675, arXiv.org, revised Nov 2016.
    4. Li Xia, 2020. "Risk‐Sensitive Markov Decision Processes with Combined Metrics of Mean and Variance," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2808-2827, December.
    5. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    6. Haoran Wang & Xun Yu Zhou, 2019. "Continuous-Time Mean-Variance Portfolio Selection: A Reinforcement Learning Framework," Papers 1904.11392, arXiv.org, revised May 2019.
    7. Haoran Wang & Shi Yu, 2021. "Robo-Advising: Enhancing Investment with Inverse Optimization and Deep Reinforcement Learning," Papers 2105.09264, arXiv.org.
    8. Xiangyu Cui & Xun Li & Yun Shi & Si Zhao, 2023. "Discrete-Time Mean-Variance Strategy Based on Reinforcement Learning," Papers 2312.15385, arXiv.org.
    9. Jingnan Fan & Andrzej Ruszczyński, 2018. "Risk measurement and risk-averse control of partially observable discrete-time Markov systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 161-184, October.
    10. Haoran Wang, 2019. "Large scale continuous-time mean-variance portfolio allocation via reinforcement learning," Papers 1907.11718, arXiv.org, revised Aug 2019.

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