Control Theory Meets POMDPs: A Hybrid Systems Approach
- Creators
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Ahmadi, Mohamadreza
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Jansen, Nils
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Wu, Bo
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Topcu, Ufuk
Abstract
Partially observable Markov decision processes (POMDPs) provide a modeling framework for a variety of sequential decision making under uncertainty scenarios in artificial intelligence (AI). Since the states are not directly observable in a POMDP, decision making has to be performed based on the output of a Bayesian filter (continuous beliefs); hence, making POMDPs intractable to solve and analyze. To overcome the complexity challenge of POMDPs, we apply techniques from the control theory. Our contributions are fourfold. 1) We begin by casting the problem of analyzing a POMDP into analyzing the behavior of a discrete-time switched system. 2) Then, in order to estimate the reachable belief space of a POMDP, i.e., the set of all possible evolutions given an initial belief distribution over the states and a set of actions and observations, we find overapproximations in terms of sublevel sets of Lyapunov-like functions. 3) Furthermore, in order to verify safety and performance requirements of a given POMDP, we formulate a barrier certificate theorem, wherein we show that if there exists a barrier certificate satisfying a set of inequalities along the solutions to the belief update equation of the POMDP, the safety and performance properties are guaranteed to hold. In both cases 2) and 3), the calculations can be decomposed and solved in parallel. 4) Finally, we show that the conditions we formulate can be computationally implemented as a set of sum-of-squares programs. We illustrate the applicability of our method by addressing two problems in active ad scheduling and machine teaching.
Additional Information
© 2020 IEEE. Manuscript received April 15, 2020; accepted October 28, 2020. Date of publication November 4, 2020; date of current version November 4, 2021. This work was supported by Grant AFOSR FA9550-19-1-0005, Grant AFRL FA9550-19-1-0169, Grant DARPA D19AP00004, Grant NSF 1646522, Grant NWO OCENW.KLEIN.187, and Grant NSF 1652113. Recommended by Associate Editor L. Palopoli. M. Ahmadi appreciates the stimulating discussions with Dr.Y. Chen at the University of Chicago, Prof. Y. Yue at Caltech, and Prof. R. M. Murray at Caltech.Attached Files
Accepted Version - 09248580.pdf
Submitted - 1905.08095.pdf
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Additional details
- Eprint ID
- 106456
- DOI
- 10.1109/tac.2020.3035755
- Resolver ID
- CaltechAUTHORS:20201105-145616123
- FA9550-19-1-0005
- Air Force Office of Scientific Research (AFOSR)
- FA9550-19-1-0169
- Air Force Research Laboratory (AFRL)
- D19AP00004
- Defense Advanced Research Projects Agency (DARPA)
- CNS-1646522
- NSF
- OCENW.KLEIN.187
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)
- CNS-1652113
- NSF
- Created
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2020-11-06Created from EPrint's datestamp field
- Updated
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2021-10-29Created from EPrint's last_modified field
- Caltech groups
- Center for Autonomous Systems and Technologies (CAST)