从分布角度看风险厌恶马尔可夫决策过程

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-07-17 DOI:10.1287/moor.2023.0211

Ziteng Cheng, Sebastian Jaimungal

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引用次数: 0

摘要

通过采用分布观点来看待不变法凸风险度量，我们在分布层面上构建了动态风险度量（DRMs）。然后，我们将这些 DRMs 应用于研究马尔可夫决策过程，其中包含了潜在成本、随机行动和弱连续的过渡核。此外，所提出的 DRM 允许风险规避发生动态变化。在温和的假设条件下，我们推导出了动态编程原理，并证明在有限和无限时间跨度内都存在最优政策。此外，我们还为确定性行动的最优性提供了充分条件。最后，我们以限价订单簿和自动驾驶的最优清算为例进行了说明：这项工作得到了加拿大自然科学与工程研究理事会 [RGPAS-2018-522715 和 RGPIN-2018-05705] 的支持。

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Risk-Averse Markov Decision Processes Through a Distributional Lens

By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamic risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent costs, random actions, and weakly continuous transition kernels. Furthermore, the proposed DRMs allow risk aversion to change dynamically. Under mild assumptions, we derive a dynamic programming principle and show the existence of an optimal policy in both finite and infinite time horizons. Moreover, we provide a sufficient condition for the optimality of deterministic actions. For illustration, we conclude the paper with examples from optimal liquidation with limit order books and autonomous driving.Funding: This work was supported by Natural Sciences and Engineering Research Council of Canada [Grants RGPAS-2018-522715 and RGPIN-2018-05705].

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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