  We study continuity and robustness properties of infinite-horizon average
expected cost problems with respect to (controlled) transition kernels, and
applications of these results to the problem of robustness of control policies
designed for approximate models applied to actual systems. We show that
sufficient conditions presented in the literature for discounted-cost problems
are in general not sufficient to ensure robustness for average-cost problems.
However, we show that the average optimal cost is continuous in the
convergences of controlled transition kernel models where convergence of models
entails (i) continuous weak convergence in state and actions, and (ii)
continuous setwise convergence in the actions for every fixed state variable,
in addition to either uniform ergodicity or some regularity conditions. We
establish that the mismatch error due to the application of a control policy
designed for an incorrectly estimated model to the true model decreases to zero
as the incorrect model approaches the true model under the stated convergence
criteria. Our findings significantly relax related studies in the literature
which have primarily considered the more restrictive total variation
convergence criteria. Applications to robustness to models estimated through
empirical data (where almost sure weak convergence criterion typically holds,
but stronger criteria do not) are studied and conditions for asymptotic
robustness to data-driven learning are established.
