NDLI: Explorer Greatest Fixed Points of Probabilistic Min / Max Polynomial Equations , and Reachability for Branching Markov Decision Processes ?

Please wait, while we are loading the content...

Explorer Greatest Fixed Points of Probabilistic Min / Max Polynomial Equations , and Reachability for Branching Markov Decision Processes ?

Content Provider	Semantic Scholar
Author	Etessami, Kousha Stewart, Alistair Yannakakis, Mihalis
Copyright Year	2016
Abstract	We give polynomial time algorithms for quantitative (and qualitative) reachability analysis for Branching Markov Decision Processes (BMDPs). Speci cally, given a BMDP, and given an initial population, where the objective of the controller is to maximize (or minimize) the probability of eventually reaching a population that contains an object of a desired (or undesired) type, we give algorithms for approximating the supremum (in mum) reachability probability, within desired precision > 0, in time polynomial in the encoding size of the BMDP and in log(1/ ). We furthermore give P-time algorithms for computing -optimal strategies for both maximization and minimization of reachability probabilities. We also give P-time algorithms for all associated qualitative analysis problems, namely: deciding whether the optimal (supremum or in mum) reachability probabilities are 0 or 1. Prior to this paper, approximation of optimal reachability probabilities for BMDPs was not even known to be decidable. Our algorithms exploit the following basic fact: we show that for any BMDP, its maximum (minimum) non-reachability probabilities are given by the greatest xed point (GFP) solution g∗ ∈ [0, 1] of a corresponding monotone max (min) Probabilistic Polynomial System of equations (max/min-PPS), x = P (x), which are the Bellman optimality equations for a BMDP with non-reachability objectives. We show how to compute the GFP of max/min PPSs to desired precision in P-time.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www.research.ed.ac.uk/portal/files/19395294/Etessami_Stewart_ET_AL_2014_Greatest_Fixed_Points_of_Probabilistic_Min_Max_Polynomial_Equations_and_Reachability_for_Branching_Markov_Decision_Processes.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in