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Properties of the QBG-value Function

Frans A. Oliehoek, Nikos Vlassis, and Matthijs T. J. Spaan. Properties of the QBG-value Function. IAS technical report IAS-UVA-07-04, Intelligent Systems Lab, University of Amsterdam, 2007.

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Abstract

In this technical report we treat some properties of the recently introduced QBG-value function. In particular we show that it is a piecewise linear and convex function over the space of joint beliefs. Furthermore, we show that there exists an optimal infinite-horizon QBG-value function, as the QBG backup operator is a contraction mapping. We conclude by noting that the optimal Dec-POMDP Q-value function cannot be defined over joint beliefs.

BibTeX Entry

@TECHREPORT{Oliehoek07TR_QBGprops,
    author =        {Frans A. Oliehoek and Nikos Vlassis 
                     and Matthijs T. J. Spaan},
    title =         {Properties of the {QBG}-value Function},
    institution =   {Intelligent Systems Lab, University of Amsterdam},
    type =          {IAS technical report},
    number =        {IAS-UVA-07-04},
    address =       {Amsterdam, The Netherlands},
    month =         feb,
    year =          2007,
    note =          {},
    keywords =      {nonrefereed, techrep},
    abstract ={
    In this technical report we treat some properties of the recently
    introduced QBG-value function. In particular we show that it
    is a piecewise linear and convex function over the space of
    joint beliefs. Furthermore, we show that there exists an optimal
    infinite-horizon QBG-value function, as the QBG backup
    operator is a contraction mapping. We conclude by noting that
    the optimal Dec-POMDP Q-value function cannot be defined over
    joint beliefs.}
}

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