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Control of Diffusions via Linear Programming

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Stochastic Programming

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 150))

Abstract

This chapter presents an approach that leverages linear programming to approximate optimal policies for controlled diffusion processes, possibly with high-dimensional state and action spaces. The approach fits a linear combination of basis functions to the dynamic programming value function; the resulting approximation guides control decisions. Linear programming is used here to compute basis function weights. This builds on the linear programming approach to approximate dynamic programming, previously developed in the context of discrete-time stochastic control.

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Notes

  1. 1.

    The term basis functions is commonly used in the approximate dynamic programming literature to refer to a set of functions that form a basis for the space from which an approximation is generated.

  2. 2.

    We experimented with the convex programming approach, but found that not to be efficient enough to address problems of practical scale.

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Author information

Authors and Affiliations

  1. Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305, USA

    Jiarui Han & Benjamin Van Roy

Authors
  1. Jiarui Han
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  2. Benjamin Van Roy
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Corresponding author

Correspondence to Benjamin Van Roy .

Editor information

Editors and Affiliations

  1. Dept. Management Science & Engineering, Stanford University, Stanford, 94305, California, USA

    Gerd Infanger

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Han, J., Van Roy, B. (2010). Control of Diffusions via Linear Programming. In: Infanger, G. (eds) Stochastic Programming. International Series in Operations Research & Management Science, vol 150. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1642-6_16

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