  When deploying machine learning solutions, they must satisfy multiple
requirements beyond accuracy, such as fairness, robustness, or safety. These
requirements are imposed during training either implicitly, using penalties, or
explicitly, using constrained optimization methods based on Lagrangian duality.
Either way, specifying requirements is hindered by the presence of compromises
and limited prior knowledge about the data. Furthermore, their impact on
performance can often only be evaluated by actually solving the learning
problem. This paper presents a constrained learning approach that adapts the
requirements while simultaneously solving the learning task. To do so, it
relaxes the learning constraints in a way that contemplates how much they
affect the task at hand by balancing the performance gains obtained from the
relaxation against a user-defined cost of that relaxation. We call this
approach resilient constrained learning after the term used to describe
ecological systems that adapt to disruptions by modifying their operation. We
show conditions under which this balance can be achieved and introduce a
practical algorithm to compute it, for which we derive approximation and
generalization guarantees. We showcase the advantages of this resilient
learning method in image classification tasks involving multiple potential
invariances and in heterogeneous federated learning.
