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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Proceedings ArticleDOI
An online primal-dual method for discounted Markov decision processes
Mengdi Wang,Yichen Chen +1 more
TL;DR: A stochastic primal-dual algorithm for solving the linear formulation of the Bellman equation and provides a thresholding procedure that recovers the exact optimal policy from the dual iterates with high probability.
Dissertation
First-order decision-theoretic planning in structured relational environments
TL;DR: The FOMDP specification is extended to succinctly capture factored actions and additive rewards while extending the exact and approximate solution techniques to directly exploit this structure.
Patent
Method for simultaneously considering customer commit dates and customer request dates
Brian T. Denton,Robert J. Milne +1 more
TL;DR: In this article, the authors present a method for achieving simultaneous consideration of multiple customer demand dates within an advanced planning system by solving a production planning model based upon the second (commit) date to produce a first solution.
Journal ArticleDOI
Approximations to Stochastic Dynamic Programs via Information Relaxation Duality
Santiago Balseiro,David B. Brown +1 more
TL;DR: In the analysis of complex stochastic dynamic programs, the authors often seek strong theoretical guarantees on the suboptimality of heuristic policies, and a common technique for obtaining performance bounds is the Fourier transform.
Journal ArticleDOI
Convergence rates of moment-sum-of-squares hierarchies for optimal control problems
TL;DR: In this article, the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data was studied.
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