Reachability and Safety Objectives in Markov Decision Processes on Long but Finite Horizons

Galit Ashkenazi-Golan (), János Flesch (), Arkadi Predtetchinski () and Eilon Solan ()
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Galit Ashkenazi-Golan: Tel-Aviv University
János Flesch: Maastricht University
Arkadi Predtetchinski: Maastricht University
Eilon Solan: Tel-Aviv University

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 3, No 14, 945-965

Abstract: Abstract We consider discrete-time Markov decision processes in which the decision maker is interested in long but finite horizons. First we consider reachability objective: the decision maker’s goal is to reach a specific target state with the highest possible probability. A strategy is said to overtake another strategy, if it gives a strictly higher probability of reaching the target state on all sufficiently large but finite horizons. We prove that there exists a pure stationary strategy that is not overtaken by any pure strategy nor by any stationary strategy, under some condition on the transition structure and respectively under genericity. A strategy that is not overtaken by any other strategy, called an overtaking optimal strategy, does not always exist. We provide sufficient conditions for its existence. Next we consider safety objective: the decision maker’s goal is to avoid a specific state with the highest possible probability. We argue that the results proven for reachability objective extend to this model.

Keywords: Markov decision process; Reachability objective; Safety objective; Overtaking optimality; Perron–Frobenius eigenvalue; 90C40 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01681-2

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