The Linear Programming Approach to Approximate Dynamic Programming
TLDR
In this article, an efficient method based on linear programming for approximating solutions to large-scale stochastic control problems is proposed. But the approach is not suitable for large scale queueing networks.Abstract:
The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits" a linear combination of pre-selected basis functions to the dynamic programming cost-to-go function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and "state-relevance weights" that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology.read more
Citations
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Fully Polynomial Time ( ; ) -Approximation Schemes for Continuous Stochastic Convex Dynamic Programs
Nir Halman,Giacomo Nannicini +1 more
TL;DR: The proposed fully polynomial time -approximation schemes for stochastic dynamic programs with continuous state and action spaces are developed, when the single-period cost functions are convex Lipschitz-continuous functions that are accessed via value oracle calls.
Journal ArticleDOI
Dynamic programming approach for fuzzy linear programming problems FLPs and its application to optimal resource allocation problems in education system
Izaz Ullah Khan,Muhammad Aftab +1 more
TL;DR: The established dynamic programming model for solving linear programming problems in a crisp environment is revised and the proposed fuzzy model takes into account uncertainty in the linear programming modeling process and is more robust, flexible and practicable.
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References
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TL;DR: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization.
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