  Overparameterization and overfitting are common concerns when designing and
training deep neural networks, that are often counteracted by pruning and
regularization strategies. However, these strategies remain secondary to most
learning approaches and suffer from time and computational intensive
procedures. We suggest a multiobjective perspective on the training of neural
networks by treating its prediction accuracy and the network complexity as two
individual objective functions in a biobjective optimization problem. As a
showcase example, we use the cross entropy as a measure of the prediction
accuracy while adopting an l1-penalty function to assess the total cost (or
complexity) of the network parameters. The latter is combined with an
intra-training pruning approach that reinforces complexity reduction and
requires only marginal extra computational cost. From the perspective of
multiobjective optimization, this is a truly large-scale optimization problem.
We compare two different optimization paradigms: On the one hand, we adopt a
scalarization-based approach that transforms the biobjective problem into a
series of weighted-sum scalarizations. On the other hand we implement
stochastic multi-gradient descent algorithms that generate a single Pareto
optimal solution without requiring or using preference information. In the
first case, favorable knee solutions are identified by repeated training runs
with adaptively selected scalarization parameters. Preliminary numerical
results on exemplary convolutional neural networks confirm that large
reductions in the complexity of neural networks with neglibile loss of accuracy
are possible.
