  The success of DNNs is driven by the counter-intuitive ability of
over-parameterized networks to generalize, even when they perfectly fit the
training data. In practice, test error often continues to decrease with
increasing over-parameterization, referred to as double descent. This allows
practitioners to instantiate large models without having to worry about
over-fitting. Despite its benefits, however, prior work has shown that
over-parameterization can exacerbate bias against minority subgroups. Several
fairness-constrained DNN training methods have been proposed to address this
concern. Here, we critically examine MinDiff, a fairness-constrained training
procedure implemented within TensorFlow's Responsible AI Toolkit, that aims to
achieve Equality of Opportunity. We show that although MinDiff improves
fairness for under-parameterized models, it is likely to be ineffective in the
over-parameterized regime. This is because an overfit model with zero training
loss is trivially group-wise fair on training data, creating an "illusion of
fairness," thus turning off the MinDiff optimization (this will apply to any
disparity-based measures which care about errors or accuracy. It won't apply to
demographic parity). Within specified fairness constraints, under-parameterized
MinDiff models can even have lower error compared to their over-parameterized
counterparts (despite baseline over-parameterized models having lower error).
We further show that MinDiff optimization is very sensitive to choice of batch
size in the under-parameterized regime. Thus, fair model training using MinDiff
requires time-consuming hyper-parameter searches. Finally, we suggest using
previously proposed regularization techniques, viz. L2, early stopping and
flooding in conjunction with MinDiff to train fair over-parameterized models.
