Markov Decision Problems Where Means Bound Variances

Alessandro Arlotto (), Noah Gans () and J. Michael Steele ()
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Alessandro Arlotto: The Fuqua School of Business, Duke University, Durham, North Carolina, 27708
Noah Gans: Operations and Information Management Department, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania, 19104
J. Michael Steele: Statistics Department, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania, 19104

Operations Research, 2014, vol. 62, issue 4, 864-875

Abstract: We identify a rich class of finite-horizon Markov decision problems (MDPs) for which the variance of the optimal total reward can be bounded by a simple linear function of its expected value. The class is characterized by three natural properties: reward nonnegativity and boundedness , existence of a do-nothing action , and optimal action monotonicity . These properties are commonly present and typically easy to check. Implications of the class properties and of the variance bound are illustrated by examples of MDPs from operations research, operations management, financial engineering, and combinatorial optimization.

Keywords: Markov decision problems; variance bounds; optimal total reward (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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