The Annals of Statistics

Averaging vs. Discounting in Dynamic Programming: a Counterexample

James Flynn

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We consider countable state, finite action dynamic programming problems with bounded rewards. Under Blackwell's optimality criterion, a policy is optimal if it maximizes the expected discounted total return for all values of the discount factor sufficiently close to 1. We give an example where a policy meets that optimality criterion, but is not optimal with respect to Derman's average cost criterion. We also give conditions under which this pathology cannot occur.

Article information

Ann. Statist., Volume 2, Number 2 (1974), 411-413.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 49C15
Secondary: 62L99: None of the above, but in this section 90C40: Markov and semi-Markov decision processes 93C55: Discrete-time systems 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]

Dynamic programming average cost criteria discounting Markov decision process


Flynn, James. Averaging vs. Discounting in Dynamic Programming: a Counterexample. Ann. Statist. 2 (1974), no. 2, 411--413. doi:10.1214/aos/1176342678.

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