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POMDPs in Continuous Time and Discrete Spaces

Alt, B. and Schultheis, M. and Koeppl, H. (2020):
POMDPs in Continuous Time and Discrete Spaces.
In: Advances in Neural Information Processing Systems 33 (NeurIPS 2020),
34th Conference on Neural Information Processing Systems, virtual Conference, 06.-12.12.2020, [Conference or Workshop Item]

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.

Item Type: Conference or Workshop Item
Erschienen: 2020
Creators: Alt, B. and Schultheis, M. and Koeppl, H.
Title: POMDPs in Continuous Time and Discrete Spaces
Language: English
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.

Title of Book: Advances in Neural Information Processing Systems 33 (NeurIPS 2020)
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
DFG-Collaborative Research Centres (incl. Transregio)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
Zentrale Einrichtungen
Zentrale Einrichtungen > Centre for Cognitive Science (CCS)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1053: MAKI – Multi-Mechanisms Adaptation for the Future Internet
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1053: MAKI – Multi-Mechanisms Adaptation for the Future Internet > B: Adaptation Mechanisms
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1053: MAKI – Multi-Mechanisms Adaptation for the Future Internet > B: Adaptation Mechanisms > Subproject B4: Planning
Event Title: 34th Conference on Neural Information Processing Systems
Event Location: virtual Conference
Event Dates: 06.-12.12.2020
Date Deposited: 26 Oct 2020 12:06
Official URL: https://proceedings.neurips.cc/paper/2020/hash/992f0fed0720d...
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