  Delta lenses are an established mathematical framework for modelling and
designing bidirectional model transformations. Following the recent
observations by Fong et al, the paper extends the delta lens framework with a a
new ingredient: learning over a parameterized space of model transformations
seen as functors. We define a notion of an asymmetric learning delta lens with
amendment (ala-lens), and show how ala-lenses can be organized into a symmetric
monoidal (sm) category. We also show that sequential and parallel composition
of well-behaved ala-lenses are also well-behaved so that well-behaved
ala-lenses constitute a full sm-subcategory of ala-lenses.
