  The existing work on the distributed training of machine learning (ML) models
has consistently overlooked the distribution of the achieved learning quality,
focusing instead on its average value. This leads to a poor dependability}of
the resulting ML models, whose performance may be much worse than expected. We
fill this gap by proposing DepL, a framework for dependable learning
orchestration, able to make high-quality, efficient decisions on (i) the data
to leverage for learning, (ii) the models to use and when to switch among them,
and (iii) the clusters of nodes, and the resources thereof, to exploit. For
concreteness, we consider as possible available models a full DNN and its
compressed versions. Unlike previous studies, DepL guarantees that a target
learning quality is reached with a target probability, while keeping the
training cost at a minimum. We prove that DepL has constant competitive ratio
and polynomial complexity, and show that it outperforms the state-of-the-art by
over 27% and closely matches the optimum.
