  This paper extends the paradigm of "mobile edge learning (MEL)" by designing
an optimal task allocation scheme for training a machine learning model in an
asynchronous manner across mutiple edge nodes or learners connected via a
resource-constrained wireless edge network. The optimization is done such that
the portion of the task allotted to each learner is completed within a given
global delay constraint and a local maximum energy consumption limit. The time
and energy consumed are related directly to the heterogeneous communication and
computational capabilities of the learners; i.e. the proposed model is
heterogeneity aware (HA). Because the resulting optimization is an NP-hard
quadratically-constrained integer linear program (QCILP), a two-step
suggest-and-improve (SAI) solution is proposed based on using the solution of
the relaxed synchronous problem to obtain the solution to the asynchronous
problem. The proposed HA asynchronous (HA-Asyn) approach is compared against
the HA synchronous (HA-Sync) scheme and the heterogeneity unaware (HU) equal
batch allocation scheme. Results from a system of 20 learners tested for
various completion time and energy consumption constraints show that the
proposed HA-Asyn method works better than the HU synchronous/asynchronous
(HU-Sync/Asyn) approach and can provide gains of up-to 25\% compared to the
HA-Sync scheme.
