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Distribution-based objectives for Markov Decision Processes

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 Blaise Genest
Tuesday, June 26 2018 at 11:00AM
Salle de Conférence (Pavillon des Jardins)
Blaise Genest (Irisa, Rennes)

Abstract: We consider distribution-based objectives for Markov Decision Processes (MDP). This class of objectives gives rise to an interesting trade-off between full and partial information. As in full observation, the strategy in the MDP can depend on the state of the system, but similar to partial information, the strategy needs to account for all the states at the same time. In this paper, we focus on two safety problems that arise naturally in this context, namely, existential and universal safety. Given an MDP A and a closed and convex polytope H of probability distributions over the states of A, the existential safety problem asks whether there exists some distribution ∆ in H and a strategy of A, such that starting from ∆ and repeatedly applying this strategy keeps the distribution forever in H. The universal safety problem asks whether for all distributions in H, there exists such a strategy of A which keeps the distribution forever in H. Further, we compare these results with existential and universal safety problems for Rabin’s probabilistic finite-state automata (PFA), the subclass of Partially Observable MDPs which have zero observation. Compared to MDPs, strategies of PFAs are not state dependent.

joint work with S. Akshay (IIT Bombay) and Nikhil Vyas (PhD student @ MIT).

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