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Toward breaking the curse of dimensionality: an FPTAS for stochastic dynamic programs with multidimensional action and scalar state

Nir Halman(halman***at***huji.ac.il)
Giacomo Nannicini(nannicini***at***us.ibm.com)

Abstract: We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex piecewise linear costs and linear state transition function. The action spaces are polyhedral and described by parametric linear programs. This type of problems finds applications in the area of optimal planning under uncertainty, and can be thought of as the problem of optimally managing a single non-discrete resource over a finite time horizon. The FPTAS relies on the solution of polynomial-sized linear programs to recursively compute an approximation of the value function at each stage. Our paper enlarges the class of dynamic programs that admit an FPTAS by showing how to deal with multidimensional action spaces and with vectors of continuous random variables with bounded support under suitable conditions, therefore getting one step closer to overcoming the curse of dimensionality of dynamic programming.

Keywords: Dynamic programming, linear programming, K-approximation sets and functions, FPTAS, approximation scheme

Category 1: Combinatorial Optimization (Approximation Algorithms )

Category 2: Other Topics (Dynamic Programming )

Category 3: Applications -- OR and Management Sciences (Supply Chain Management )

Citation:

Download: [PDF]

Entry Submitted: 07/14/2017
Entry Accepted: 07/14/2017
Entry Last Modified: 07/14/2017

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