Journal of Convex Analysis 33 (2026), No. 1&2, 393--413
Copyright Heldermann Verlag 2026
Epi-Consistent Approximationof Stochastic Dynamic Programs
Dominic S. T. Keehan
University of Auckland, New Zealand
dkee331@aucklanduni.ac.nz
Johannes O. Royset
University of Southern California, Los Angeles, U.S.A.
royset@usc.edu
We study the consistency of stochastic dynamic programs under converging probability distributions and other approximations. Utilizing results on the epi-convergence of expectation functions with varying measures and integrands, and the Attouch-Wets distance, we show that appropriate equi-semicontinuity assumptions assure epi-consistency. A number of examples illustrate the approach. In particular, we permit both unbounded and simultaneously approximated stage-cost functions, and treat an example with approximated constraints.
Keywords: Stochastic optimal control, stochastic dynamic programming, epi-convergence, Attouch-Wets distance.
MSC: 90C15; 90C39.
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