  In this paper we revisit the fixed-confidence identification of the Pareto
optimal set in a multi-objective multi-armed bandit model. As the sample
complexity to identify the exact Pareto set can be very large, a relaxation
allowing to output some additional near-optimal arms has been studied. In this
work we also tackle alternative relaxations that allow instead to identify a
relevant subset of the Pareto set. Notably, we propose a single sampling
strategy, called Adaptive Pareto Exploration, that can be used in conjunction
with different stopping rules to take into account different relaxations of the
Pareto Set Identification problem. We analyze the sample complexity of these
different combinations, quantifying in particular the reduction in sample
complexity that occurs when one seeks to identify at most $k$ Pareto optimal
arms. We showcase the good practical performance of Adaptive Pareto Exploration
on a real-world scenario, in which we adaptively explore several vaccination
strategies against Covid-19 in order to find the optimal ones when multiple
immunogenicity criteria are taken into account.
