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POMDPs in Continuous Time and Discrete Spaces

Alt, B. ; Schultheis, M. ; Koeppl, H. (2020)
POMDPs in Continuous Time and Discrete Spaces.
34th Conference on Neural Information Processing Systems. virtual Conference (06.-12.12.2020)
Konferenzveröffentlichung, Bibliographie

Kurzbeschreibung (Abstract)

Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space systems under partial observability. This places our work at the intersection of optimal filtering and optimal control. At the current state of research, a mathematical description for simultaneous decision making and filtering in continuous time with finite state and action spaces is still missing. In this paper, we give a mathematical description of a continuous-time partial observable Markov decision process (POMDP). By leveraging optimal filtering theory we derive a Hamilton-Jacobi-Bellman (HJB) type equation that characterizes the optimal solution. Using techniques from deep learning we approximately solve the resulting partial integro-differential equation. We present (i) an approach solving the decision problem offline by learning an approximation of the value function and (ii) an online algorithm which provides a solution in belief space using deep reinforcement learning. We show the applicability on a set of toy examples which pave the way for future methods providing solutions for high dimensional problems.

Typ des Eintrags: Konferenzveröffentlichung
Erschienen: 2020
Autor(en): Alt, B. ; Schultheis, M. ; Koeppl, H.
Art des Eintrags: Bibliographie
Titel: POMDPs in Continuous Time and Discrete Spaces
Sprache: Englisch
Publikationsjahr: 22 Oktober 2020
Buchtitel: Advances in Neural Information Processing Systems 33 (NeurIPS 2020)
Veranstaltungstitel: 34th Conference on Neural Information Processing Systems
Veranstaltungsort: virtual Conference
Veranstaltungsdatum: 06.-12.12.2020
URL / URN: https://proceedings.neurips.cc/paper/2020/hash/992f0fed0720d...
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Kurzbeschreibung (Abstract):

Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space systems under partial observability. This places our work at the intersection of optimal filtering and optimal control. At the current state of research, a mathematical description for simultaneous decision making and filtering in continuous time with finite state and action spaces is still missing. In this paper, we give a mathematical description of a continuous-time partial observable Markov decision process (POMDP). By leveraging optimal filtering theory we derive a Hamilton-Jacobi-Bellman (HJB) type equation that characterizes the optimal solution. Using techniques from deep learning we approximately solve the resulting partial integro-differential equation. We present (i) an approach solving the decision problem offline by learning an approximation of the value function and (ii) an online algorithm which provides a solution in belief space using deep reinforcement learning. We show the applicability on a set of toy examples which pave the way for future methods providing solutions for high dimensional problems.

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Erstveröffentlichung

Fachbereich(e)/-gebiet(e): 18 Fachbereich Elektrotechnik und Informationstechnik
18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik > Bioinspirierte Kommunikationssysteme
18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik
DFG-Sonderforschungsbereiche (inkl. Transregio)
DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche
Zentrale Einrichtungen
Zentrale Einrichtungen > Centre for Cognitive Science (CCS)
DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1053: MAKI – Multi-Mechanismen-Adaption für das künftige Internet
DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1053: MAKI – Multi-Mechanismen-Adaption für das künftige Internet > B: Adaptionsmechanismen
DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1053: MAKI – Multi-Mechanismen-Adaption für das künftige Internet > B: Adaptionsmechanismen > Teilprojekt B4: Planung
Hinterlegungsdatum: 26 Okt 2020 12:06
Letzte Änderung: 04 Apr 2023 13:02
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