  The multi-task learning (MTL) paradigm can be traced back to an early paper
of Caruana (1997) in which it was argued that data from multiple tasks can be
used with the aim to obtain a better performance over learning each task
independently. A solution of MTL with conflicting objectives requires modelling
the trade-off among them which is generally beyond what a straight linear
combination can achieve. A theoretically principled and computationally
effective strategy is finding solutions which are not dominated by others as it
is addressed in the Pareto analysis. Multi-objective optimization problems
arising in the multi-task learning context have specific features and require
adhoc methods. The analysis of these features and the proposal of a new
computational approach represent the focus of this work. Multi-objective
evolutionary algorithms (MOEAs) can easily include the concept of dominance and
therefore the Pareto analysis. The major drawback of MOEAs is a low sample
efficiency with respect to function evaluations. The key reason for this
drawback is that most of the evolutionary approaches do not use models for
approximating the objective function. Bayesian Optimization takes a radically
different approach based on a surrogate model, such as a Gaussian Process. In
this thesis the solutions in the Input Space are represented as probability
distributions encapsulating the knowledge contained in the function
evaluations. In this space of probability distributions, endowed with the
metric given by the Wasserstein distance, a new algorithm MOEA/WST can be
designed in which the model is not directly on the objective function but in an
intermediate Information Space where the objects from the input space are
mapped into histograms. Computational results show that the sample efficiency
and the quality of the Pareto set provided by MOEA/WST are significantly better
than in the standard MOEA.
