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Speaker(s): Laurent Doyen
Affiliation: CNRS & LSV, ENS Paris-Saclay
Date: Nov. 14, 2018, 2:15 p.m.
Room: room 5050
Seminar: Seminar Automata Theory

A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon in not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary, to represent the worst-case scenario.

A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon T, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping time distribution with expected stopping time T, then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping time distribution can be achieved in polynomial time. Consequently, our polynomial-time algorithm for adversarial stopping time also computes an optimal plan among all possible plans.

It will be long version of the talk presented at Highlights 2018: Highlights of Logic, Games and Automata.

Graph Planning with Expected Finite Horizon

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