  The main objective of this paper is to outline a theoretical framework to
analyse how humans' decision-making strategies under uncertainty manage the
trade-off between information gathering (exploration) and reward seeking
(exploitation). A key observation, motivating this line of research, is the
awareness that human learners are amazingly fast and effective at adapting to
unfamiliar environments and incorporating upcoming knowledge: this is an
intriguing behaviour for cognitive sciences as well as an important challenge
for Machine Learning. The target problem considered is active learning in a
black-box optimization task and more specifically how the
exploration/exploitation dilemma can be modelled within Gaussian Process based
Bayesian Optimization framework, which is in turn based on uncertainty
quantification. The main contribution is to analyse humans' decisions with
respect to Pareto rationality where the two objectives are improvement expected
and uncertainty quantification. According to this Pareto rationality model, if
a decision set contains a Pareto efficient (dominant) strategy, a rational
decision maker should always select the dominant strategy over its dominated
alternatives. The distance from the Pareto frontier determines whether a choice
is (Pareto) rational (i.e., lays on the frontier) or is associated to
"exasperate" exploration. However, since the uncertainty is one of the two
objectives defining the Pareto frontier, we have investigated three different
uncertainty quantification measures and selected the one resulting more
compliant with the Pareto rationality model proposed. The key result is an
analytical framework to characterize how deviations from "rationality" depend
on uncertainty quantifications and the evolution of the reward seeking process.
