The analysis of shooting problems via generalised bandits
Glazebrook, Kevin D.
Mitchell, Helen M.
Gaver, Donald P.
Jacobs, Patricia A.
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A single Red wishes to shoot at a collection of Blue targets in order to maximize some measure of return obtained from Blues killed before Red's own demise. While the class of decision processes called multi-armed bandits has been previously deployed to develop optimal policies for Red, we argue the importance of a little known, but more general class of bandit processes introduced by Nash (1980). In particular, the deployment of this class of processes will enable Red to take account in a natural way of the relative threats posed to his own survival in taking targeting actions. We develop optimal shooting policies for Red in the context of a range of models, which are of independent interest. The paper concludes with a numerical study.
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NPS Report NumberNPS-OR-04-005