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A multiple criteria Markovian Decision Process Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/6108vf02x

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  • A composite system of a Markovian Decision Process with multiple criteria involves both discounting criteria and nondiscounting criteria. The measurement of the discounting criteria is chosen to be the total sum of the payoffs over the time horizon and the measurement of the non-discounting criteria is chosen to be the average long-run expected payoffs per period. The intent of this study is to present a system formulation to a finite state time infinite Markovian Decision Process with multiple criteria in an attempt to establish a solution procedure which could apply to most of the situations where the availability of generating information from the decision making entity varies. Binary variables are introduced for each action at each state and then a mixed binary program is developed to find an overall optimal policy. A structural relationship between the system of Markovian Decision Process (MDP) with discounting and the system of MDP with no discounting is examined and a sufficient condition of assigning the initial distribution for MDP with discounting is obtained to eliminate the difficulties in inter-relating these two different systems. Additionally, a method of generating a multiple objective linear program (MOLP) corresponding to each policy is presented. The optimality conditions are then extended to the MOLP for the non-dominated policies to transform the system into the vector maximum problem. Finally, a sequence of linear approximation of the utility is illustrated. The development and discussion of the theoretical questions is clarified by examples where the discussed system is most applicable. System formulations for the examples are also provided along with the post-optimal analysis.
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