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The Optimal Control of Partially Observable Markov Processes over a Finite Horizon
Abstract
This paper formulates the optimal control problem for a class of mathematical models in which the system to be controlled is characterized by a finite-state discrete-time Markov process. The states of this internal process are not directly observable by the controller; rather, he has available a set of observable outputs that are only probabilistically related to the internal state of the system. The formulation is illustrated by a simple machine-maintenance example, and other specific application areas are also discussed. The paper demonstrates that, if there are only a finite number of control intervals remaining, then the optimal payoff function is a piecewise-linear, convex function of the current state probabilities of the internal Markov process. In addition, an algorithm for utilizing this property to calculate the optimal control policy and payoff function for any finite horizon is outlined. These results are illustrated by a numerical example for the machine-maintenance problem.
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Cited by
Planning and acting in partially observable stochastic domains
Kaelbling, L. P., Littman, M. L., & Cassandra, A. R. (1998) · Artificial Intelligence · doi:10.1016/s0004-3702(98)00023-x · Cited by 4,149
The Complexity of Markov Decision Processes
Papadimitriou, C. H., & Tsitsiklis, J. N. (1987) · Mathematics of Operations Research · doi:10.1287/moor.12.3.441 · Cited by 1,329
A survey of maintenance models: The control and surveillance of deteriorating systems
Pierskalla, W. P., & Voelker, J. A. (1976) · Naval Research Logistics Quarterly · doi:10.1002/nav.3800230302 · Cited by 678
A Survey of Multi-Objective Sequential Decision-Making
Roijers, D. M., Vamplew, P., Whiteson, S., & Dazeley, R. (2013) · Journal of Artificial Intelligence Research · doi:10.1613/jair.3987 · Cited by 461
Cooperative Inverse Reinforcement Learning
Hadfield-Menell, D., Dragan, A., Abbeel, P., & Russell, S. (2016) · arXiv · doi:10.48550/arxiv.1606.03137 · Cited by 413
Metadata
- Authors
- Smallwood, R. D., & Sondik, E. J.
- Venue
- Operations Research
- Published
- 1973-10
- Volume
- 21
- Issue
- 5
- Pages
- 1071-1088
- ISSN
- 0030-364X (ISSN-L)
- 1526-5463
- OpenAlex
- W2034725503
- Cited by
- 1,479
- References
- 0
- FWCI
- 44.76
- Type
- journal article
- Language
- en
- Open access
- closed
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- Smallwood, R. D., & Sondik, E. J. (1973). The Optimal Control of Partially Observable Markov Processes over a Finite Horizon. Operations Research. https://doi.org/10.1287/opre.21.5.1071
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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