Date of this Version
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.
Markov decision problems, variance bounds, optimal total reward
Arlotto, A., Gans, N., & Steele, J. M. (2014). Markov Decision Problems Where Means Bound Variances. Operations Research, 62 (4), 864-875. http://dx.doi.org/10.1287/opre.2014.1281
Date Posted: 27 November 2017
This document has been peer reviewed.