The Linear Programming Approach to Reach-Avoid Problems for Markov Decision Processes
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Date
2017Type
- Journal Article
Abstract
One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a control policy to maximize the probability of reaching a target set at a given time, while staying in a safe set at all prior times. We characterize the solution to this problem through an infinite dimensional linear program. We then develop a tractable approximation to the infinite dimensional linear program through finite dimensional approximations of the decision space and constraints. For a large class of Markov decision processes modeled by Gaussian mixtures kernels we show that through a proper selection of the finite dimensional space, one can further reduce the computational complexity of the resulting linear program. We validate the proposed method and analyze its potential with numerical case studies. Show more
Publication status
publishedExternal links
Journal / series
Journal of Artificial Intelligence ResearchVolume
Pages / Article No.
Publisher
Morgan KaufmannSubject
Reachability; Approximate dynamic programming; Markov decision processes; Stochastic controlOrganisational unit
03751 - Lygeros, John / Lygeros, John
09578 - Kamgarpour, Maryam (ehemalig) / Kamgarpour, Maryam (former)
Funding
137876 - Feedback control of camera networks for tracking and surveillance (SNF)
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