Title: Multi-objective Bandits: Optimizing the Generalized Gini Index,
Abstract: We study the multi-armed bandit (MAB) problem where the agent receives a
vectorial feedback that encodes many possibly competing objectives to be
optimized. The goal of the agent is to find a policy, which can optimize these
objectives simultaneously in a fair way. This multi-objective online
optimization problem is formalized by using the Generalized Gini Index (GGI)
aggregation function. We propose an online gradient descent algorithm which
exploits the convexity of the GGI aggregation function, and controls the
exploration in a careful way achieving a distribution-free regret
$\tilde{\bigO} (T^{-1/2} )$ with high probability. We test our algorithm on
synthetic data as well as on an electric battery control problem where the goal
is to trade off the use of the different cells of a battery in order to balance
their respective degradation rates.