Risk-sensitive control, single controller games and linear programming

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Journal of Dynamics and Games Pub Date : 2023-10-26 DOI:10.3934/jdg.2023024
V. Borkar
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Abstract

This article recalls the recent work on a linear programming formulation of infinite horizon risk-sensitive control via its equivalence with a single controller game, using a classic work of Vrieze. This is then applied to a constrained risk-sensitive control problem with a risk-sensitive cost and risk-sensitive constraint. This facilitates a Lagrange multiplier based resolution thereof. In the process, this leads to an unconstrained linear program and its dual, parametrized by a parameter that is a surrogate for Lagrange multiplier. This also opens up the possibility of a primal - dual type numerical scheme wherein the linear program is a subroutine within the subgradient ascent based update rule for the Lagrange multiplier. This equivalent unconstrained risk-sensitive control formulation does not seem obvious without the linear programming equivalents as intermediaries. We also discuss briefly other related algorithmic possibilities for future research.
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风险敏感控制、单控制器博弈和线性规划
本文利用 Vrieze 的经典著作,通过与单控制器博弈的等价性,回顾了近期关于无限视距风险敏感控制的线性规划表述的工作。然后将其应用于具有风险敏感成本和风险敏感约束的约束风险敏感控制问题。这有助于基于拉格朗日乘数的解决方法。在此过程中,会产生一个无约束线性程序及其对偶程序,该程序的参数是拉格朗日乘数的代用参数。这也为原始-对偶型数值方案提供了可能性,其中线性程序是基于子梯度上升的拉格朗日乘法器更新规则中的一个子程序。如果没有线性规划等价物作为中介,这种等价的无约束风险敏感控制表述似乎并不明显。我们还简要讨论了未来研究的其他相关算法可能性。
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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