Epi-Consistent Approximation of Stochastic Dynamic Programs

TL;DR

This paper investigates the conditions under which stochastic dynamic programs remain consistent when their probability distributions and other components are approximated, ensuring reliable solutions in complex stochastic settings.

Contribution

It introduces a framework using epi-convergence and the Attouch--Wets distance to guarantee epi-consistency under various approximation scenarios, including unbounded costs and constraints.

Findings

Epi-convergence ensures consistency of approximated stochastic programs.

The approach handles unbounded and approximated stage-cost functions.

Examples demonstrate the applicability of the theoretical results.

Abstract

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.