Sequential learning of the Pareto front for multi-objective bandits

We study the problem of sequential learning of the Pareto front in multi-objective multi-armed bandits. An agent is faced with $K$ possible arms to pull. At each turn she picks one, and receives a vector-valued reward. When she thinks she has enough information to identify the Pareto front of the different arm means, she stops the game and gives an answer. We are interested in designing algorithms such that the answer given is correct with probability at least $1-\delta$. Our main contribution is an efficient implementation of an algorithm achieving the optimal sample complexity when the risk $\delta$ is small. With $K$ arms in $d$ dimensions, $p$ of which are in the Pareto set, the algorithm runs in time $O(K p^d)$ per round.