  In the context of the linear programming (LP) approach to data-driven
control, one assumes that the dynamical system is unknown but can be observed
indirectly through data on its evolution. Both theoretical and empirical
evidence suggest that a desired suboptimality gap is often only achieved with
massive exploration of the state-space. In case of linear systems, we discuss
how a relatively small but sufficiently rich dataset can be exploited to
generate new constraints offline and without observing the corresponding
transitions. Moreover, we show how to reconstruct the associated unknown
stage-costs and, when the system is stochastic, we offer insights on the
related problem of estimating the expected value in the Bellman operator
without re-initializing the dynamics in the same state-input pairs.
