From Infinite to Finite Programs : Explicit Error Bounds with Applications to Approximate Dynamic Programming

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2018
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Mohajerin Esfahani, Peyman
Kuhn, Daniel
Lygeros, John
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SIAM Journal on Optimization. Society for Industrial and Applied Mathematics (SIAM). 2018, 28(3), S. 1968-1998. ISSN 1052-6234. eISSN 1095-7189. Verfügbar unter: doi: 10.1137/17M1133087
Zusammenfassung

We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite dimensional LP to tractable finite convex programs in which the performance of the approximation is quantified explicitly. To this end, we adopt the recent developments in two areas of randomized optimization and first-order methods, leading to a priori as well as a posteriori performance guarantees. We illustrate the generality and implications of our theoretical results in the special case of the long-run average cost and discounted cost optimal control problems in the context of Markov decision processes on Borel spaces. The applicability of the theoretical results is demonstrated through a fisheries management problem.

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ISO 690MOHAJERIN ESFAHANI, Peyman, Tobias SUTTER, Daniel KUHN, John LYGEROS, 2018. From Infinite to Finite Programs : Explicit Error Bounds with Applications to Approximate Dynamic Programming. In: SIAM Journal on Optimization. Society for Industrial and Applied Mathematics (SIAM). 2018, 28(3), S. 1968-1998. ISSN 1052-6234. eISSN 1095-7189. Verfügbar unter: doi: 10.1137/17M1133087
BibTex
@article{MohajerinEsfahani2018Infin-55608,
  year={2018},
  doi={10.1137/17M1133087},
  title={From Infinite to Finite Programs : Explicit Error Bounds with Applications to Approximate Dynamic Programming},
  number={3},
  volume={28},
  issn={1052-6234},
  journal={SIAM Journal on Optimization},
  pages={1968--1998},
  author={Mohajerin Esfahani, Peyman and Sutter, Tobias and Kuhn, Daniel and Lygeros, John}
}
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