On the limits of using randomness to break a dynamic program's curse of dimensionality

27 Pages Posted: 30 Jul 2019 Last revised: 29 Jun 2020

Date Written: June 26, 2020

Abstract

Rust (1997) discovered a class of dynamic programs that can be solved in polynomial time with a randomized algorithm. Insulated from the curse of dimensionality, this walled garden of tractable dynamic problems is intriguing, if not useful. Unfortunately, I find that the class is more limited than we initially thought, as it requires all but a vanishingly small fraction of state variables to behave arbitrarily similarly to i.i.d. uniform random variables. However, in this special case, his approach can be tremendously powerful.

Keywords: Markov decision process, dynamic program, curse of dimensionality, random Bellman operator, random value iteration, empirical processes

Suggested Citation

Bray, Robert, On the limits of using randomness to break a dynamic program's curse of dimensionality (June 26, 2020). Available at SSRN: https://ssrn.com/abstract=3427401 or http://dx.doi.org/10.2139/ssrn.3427401

Robert Bray (Contact Author)

Northwestern University - Department of Managerial Economics and Decision Sciences (MEDS) ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

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