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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Linear programming formulation for non-stationary, finite-horizon Markov decision process models
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Relaxation Analysis for the Dynamic Knapsack Problem with Stochastic Item Sizes
Daniel Blado,Alejandro Toriello +1 more
TL;DR: A version of the knapsack problem in which an item size is random and revealed only when the decision maker attempts to insert it is considered.
References
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