Bandit Pareto Set Identification: the Fixed Budget Setting
Cyrille Kone Emilie Kaufmann Laura Richert
We study a multi-objective pure exploration problem in a multi-armed bandit
model. Each arm is associated to an unknown multi-variate distribution and the
goal is to identify the distributions whose mean is not uniformly worse than
that of another distribution: the Pareto optimal set. We propose and analyze
the first algorithms for the \emph{fixed budget} Pareto Set Identification
task. We propose Empirical Gap Elimination, a family of algorithms combining a
careful estimation of the ``hardness to classify'' each arm in or out of the
Pareto set with a generic elimination scheme. We prove that two particular
instances, EGE-SR and EGE-SH, have a probability of error that decays
exponentially fast with the budget, with an exponent supported by an
information theoretic lower-bound. We complement these findings with an
empirical study using real-world and synthetic datasets, which showcase the
good performance of our algorithms.