Parameter-Free Sampled Fictitious Play for Solving Deterministic Dynamic Programming Problems

Irina S. Dolinskaya (), Marina A. Epelman (), Esra Şişikoğlu Sir () and Robert L. Smith ()
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Irina S. Dolinskaya: Northwestern University
Marina A. Epelman: University of Michigan
Esra Şişikoğlu Sir: Office of Access Management, Mayo Clinic
Robert L. Smith: University of Michigan

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 2, No 14, 655 pages

Abstract: Abstract In this paper, we present a parameter-free variation of the Sampled Fictitious Play algorithm that facilitates fast solution of deterministic dynamic programming problems. Its random tie-breaking procedure imparts a natural randomness to the algorithm which prevents it from “getting stuck” at a local optimal solution and allows the discovery of an optimal path in a finite number of iterations. Furthermore, we illustrate through an application to maritime navigation that, in practice, a parameter-free Sampled Fictitious Play algorithm finds a high-quality solution after only a few iterations, in contrast with traditional methods.

Keywords: Sampled fictitious play; Dynamic programming; Maritime navigation; 90C39; 91A80; 68W10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0798-5

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