Gradient-Bounded Dynamic Programming with Submodular and Concave Extensible Value Functions
| Autor: | Denis Lebedev, Kostas Margellos, Paul J. Goulart |
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| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Computer science 020208 electrical & electronic engineering 02 engineering and technology Extensibility Direct computation Dual (category theory) Submodular set function Dynamic programming 020901 industrial engineering & automation Control and Systems Engineering Optimization and Control (math.OC) Bellman equation Bounded function 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Mathematics - Optimization and Control Value (mathematics) |
| DOI: | 10.48550/arxiv.2005.11213 |
| Popis: | We consider dynamic programming problems with finite, discrete-time horizons and prohibitively high-dimensional, discrete state-spaces for direct computation of the value function from the Bellman equation. For the case that the value function of the dynamic program is concave extensible and submodular in its state-space, we present a new algorithm that computes deterministic upper and stochastic lower bounds of the value function similar to dual dynamic programming. We then show that the proposed algorithm terminates after a finite number of iterations. Finally, we demonstrate the efficacy of our approach on a high-dimensional numerical example from delivery slot pricing in attended home delivery. Comment: 6 pages, 2 figures, accepted for IFAC World Congress 2020 |
| Databáze: | OpenAIRE |
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